Study on submanifolds in generalized Sasakian-space-forms with various connections.
problem Analyzing submanifolds in generalized Sasakian-space-forms with different connections.
method Examines submanifolds in generalized Sasakian-space-forms with semisymmetric metric, non-metric, Schouten-van Kampen, and Tanaka-webster connections.
result Provides results on submanifolds in generalized Sasakian-space-forms with respect to various connections.
Study invariant and anti-invariant submanifolds in special quasi-Sasakian manifolds.
problem Characterize invariant and anti-invariant submanifolds in special quasi-Sasakian manifolds.
method Investigate Chaki-pseudo parallel and Deszcz-pseudo parallel invariant submanifolds with Levi-Civita and semisymmetric metric connections. Also study invariant and anti-invariant submanifolds with Ricci solitons.
result Invariant and anti-invariant submanifolds are equivalent under certain conditions.
Study on submanifolds in specific geometric spaces.
problem Analysis of submanifolds in generalized Sasakian-space-forms.
method Examines almost semi-invariant submanifolds with various connections.
result Provides new results on submanifolds with respect to different connections.
Study on pseudo parallel contact CR-submanifolds in Kenmotsu manifolds.
problem Characterizing pseudo parallel contact CR-submanifolds in Kenmotsu manifolds.
method Analysis of pseudo parallel contact CR-submanifolds with respect to both Levi-Civita and semisymmetric metric connections in Kenmotsu manifolds.
result Equivalent conditions for pseudo parallel contact CR-submanifolds in Kenmotsu manifolds.
The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.
problem Characterizing Einstein doubly warped product manifolds with a semi-symmetric metric connection.
method Deriving curvature formulas and proving necessary and sufficient conditions for a manifold to be a warped product.
result Obtained results for Einstein doubly warped product manifolds and Einstein-like doubly warped product manifolds.
Classifies weakly Einstein submanifolds in space forms satisfying specific equalities.
problem Characterizing submanifolds in space forms with certain geometric properties.
method Classification based on Chen's equality and semisymmetric conditions.
result Classification of weakly Einstein submanifolds in space forms.
The study characterizes locally φ-semisymmetric Kenmotsu manifolds.
problem Understanding the properties of Kenmotsu manifolds.
method Characterization through local φ-semisymmetry.
result Characterization of locally φ-semisymmetric Kenmotsu manifolds.
(N(k),ξ)-semi-Riemannian manifolds are defined. Examples and properties of (N(k),ξ)-semi-Riemannian manifolds are given. Some relations involving Ta-curvature tensor in (N(k),ξ)-semi-Riemannian manifolds are proved. ξ-Ta-flat (N(k),ξ)-semi-Riemannian manifolds are defined. It is proved…
The paper investigates various generalizations of semisymmetric and pseudosymmetric manifolds.
problem Exploring different curvature tensor generalizations of semisymmetric and pseudosymmetric manifolds.
method Systematic review and examination of geometric structures with physical examples.
result Proper existence of various geometric structures, including Ricci pseudosymmetric manifolds.
Investigates curvature properties of generalized pp-wave metric.
problem Examines curvature characteristics of generalized pp-wave metric.
method Analyzes Ricci, quasi-Einstein, and pseudosymmetric properties.
result Shows various curvature properties and sufficient conditions.
Investigates curvature properties of special pure radiation metrics.
problem Analyzes the curvature of specific pure radiation spacetimes.
method Examines curvature properties of special pure radiation metrics using conformal relations and tensor analysis.
result Shows that special pure radiation spacetimes are semisymmetric, Ricci simple, and R-space.
The study characterizes symmetries in Kaehler manifolds.
problem Understanding symmetries in Kaehler manifolds.
method Analyzing specific types of Kaehler manifolds: constant holomorphic sectional curvature, semisymmetric, and holomorphically pseudosymmetric.
result Characterization results and geometric interpretation of the complex Tachibana tensor.
The paper studies (ε)-para-Sasakian 3-manifolds with Z-symmetry conditions.
problem Characterizing (ε)-para-Sasakian 3-manifolds under Z-symmetry conditions. method Examining various Z-symmetric conditions on (ε)-para-Sasakian 3-manifolds. result Characterizations of Z-symmetric, Z-semisymmetric, Z-pseudosymmetric, and projectively Z-semisymmetric conditions. The projective curvature tensor P is invariant under a geodesic preserving transformation on a semi-Riemannian manifold. It is well known that P is not a generalized curvature tensor and hence it possesses different geometric properties than other generalized curvature tensors. The main object of the present paper …
The present paper deals with the proper existence of a generalized class of recurrent manifolds, namely, hyper-generalized recurrent manifolds. We have established the proper existence of various generalized notions of recurrent manifolds. For this purpose we have presented a metric and computed its curvature propertie…
In this paper we introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a…
The paper examines curvature properties of charged Nariai spacetimes.
problem Investigating geometric structures of charged Nariai spacetimes.
method Analyzing curvature properties and geometric structures of charged Nariai spacetimes.
result Charged Nariai spacetimes are locally symmetric, 2-quasi-Einstein, and Ein(2)-space.
Generalizing the notion of local φ-symmetry of Takahashi, in the present paper, we introduce the notion of local φ-semisymmetry of a Sasakian manifold along with its proper existence and characterization. We also study the notion of local Ricci (resp., projective, conformal) φ-semisymmetry of a Sasakian manifold …
The paper explores symmetries in Kähler manifolds using Ricci tensor properties.
problem Investigating symmetries in Kähler manifolds involving Ricci tensor.
method Analyzing properties of Kähler-Einstein spaces and their generalizations.
result Clarified the geometric role of holomorphic Ricci pseudosymmetry and established new criteria for Kähler manifolds to be Einstein.
A manifold's canonical involution defines a projection of connections.
problem Defining a projection of connections on (J2=±1)-metric manifolds. method Introducing a canonical involution to project connections.
result The projection sends Levi Civita to first canonical connection.
Defines semi-symmetric metric connection on super warped products.
problem Computing curvature and Ricci tensors on super warped products.
method Introduced semi-symmetric metric connection and conditions for Einstein spaces.
result Conditions for super warped product spaces to be Einstein with semi-symmetric metric connection.
The paper studies para-Sasaki-like manifolds with a new metric connection.
problem Investigating new geometric structures on para-Sasaki-like manifolds.
method Deriving relations between connections, analyzing curvature tensors, studying solitons, constructing examples.
result Derived relations and properties of para-Sasaki-like manifolds with the generalized symmetric metric connection.
Study non-integrable distributions with various affine connections.
problem Characterize non-integrable distributions in Riemannian manifolds with different connections.
method Obtain Gauss, Codazzi, and Ricci equations for non-integrable distributions with semi-symmetric metric, non-metric, and statistical connections.
result Find new examples of Einstein and distributions with constant scalar curvature.
The study investigates properties of a specific Riemannian manifold with a semi-symmetric non-metric connection.
problem Characterizing properties of a Riemannian manifold with a semi-symmetric non-metric connection.
method Construction of a non-trivial example, proving manifold properties based on the metric being a gradient soliton or Yamabe soliton.
result A manifold with a semi-symmetric non-metric connection and gradient Ricci/Yamabe soliton is of constant curvature.
The paper studies special warped products with a specific connection on super Riemannian manifolds.
problem Investigating curvature and Ricci tensors on super warped product spaces with a semi-symmetric non-metric connection.
method Defined a semi-symmetric non-metric connection, computed curvature and Ricci tensors, and introduced and analyzed two types of super warped product spaces.
result Conditions for two super warped product spaces with a semi-symmetric non-metric connection to be Einstein spaces are provided.
New approach connects Finsler geometry's metric and connections.
problem Deriving Finsler geometry's metric and connections from compatibility axioms.
method Compatibility axioms between metric and Finsler connection.
result Metrical formulation of Finsler geometry for field theory.
Classifies connections on Galilei manifolds, generalizing known results.
problem Classifying general affine connections on Galilei manifolds.
method Classification through tensor fields, extending known Galilei connections.
result Additional freedom in connections not metric-compatible, linked to clock form and space metric.
New type of semi-symmetric non-metric connection studied in almost contact metric manifolds.
problem Exploring new types of semi-symmetric non-metric connections in geometric structures.
method Definition and properties of a new semi-symmetric non-metric connection in almost contact metric manifolds.
result Properties of the new semi-symmetric non-metric connection and covariant almost analytic vector field.
Researchers found invariant metric connections on Berger spheres that are Einstein with skew torsion.
problem Determining invariant metric affine connections on Berger spheres that are Einstein with skew torsion.
method Explicitly determined and expressed connections in both Riemannian and Lorentzian signatures.
result Every Berger sphere with Lorentzian signature admits invariant metric affine connections Einstein with skew-torsion up to S3. Study η-Ricci solitons on Kenmotsu manifolds with generalized symmetric metric connection.
problem Exploring η-Ricci solitons on Kenmotsu manifolds with a specific type of metric connection. method Examined Ricci and η-Ricci solitons on Kenmotsu manifolds with generalized symmetric metric connection of type (α,β) under various conditions. result Constructed an example of a Kenmotsu manifold with generalized symmetric metric connection of type (α,β) admitting η-Ricci solitons. For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear connections that can be associated with a system of SODE and a generalized Lagrange struc…
Connected space of Dirac-minimal metrics in 2 and 4 dimensions.
problem Finding metrics with optimal index bounds.
method Using index theory and Dirac operator properties.
result Space of Dirac-minimal metrics is connected in dimensions 2 and 4.
Families of linear connections are constructed on almost contact manifolds with Norden metric. An analogous connection to the symmetric Yano connection is obtained on a normal almost contact manifold with Norden metric and closed structural 1-form. The curvature properties of this connection are studied on two basic cl…
The paper studies geometric structures of wormholes using a new connection.
problem Exploring new geometric properties of wormholes.
method Extended Levi-Civita connection to semi-symmetric non-metric connections.
result Morris-Thorne wormholes exhibit specific geometric properties.
New connections found with specific torsion properties.
problem Understanding metric connections with specific torsion properties.
method Described Lorentzian manifolds with metric connections having parallel, skew-symmetric torsion.
result Found new Lorentzian manifolds with metric connections having parallel, skew-symmetric torsion.
The paper studies ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds.
problem Exploring ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds. method Analyzing curvature properties and developing soliton characteristics with respect to quarter-symmetric metric connection.
result Characteristics and nature of ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds. Classifies Finslerian metrics locally conformally R-Einstein.
problem Characterizing Finslerian metrics with specific curvature properties.
method Using the pulled-back tangent bundle approach to Finslerian Geometry, an intrinsic characterization of R-Einstein metrics is given, leading to the classification of locally conformally R-Einstein metrics.
result Finslerian metrics locally conformally R-Einstein are classified.
The Chern sectional curvature of a Hermitian manifold is derived and related to Kähler metrics.
problem Understanding the relationship between Chern and Riemann sectional curvatures on Hermitian manifolds.
method Derivation of Chern sectional curvature expressions and subsequent results on Ricci and scalar curvatures.
result A Hermitian metric is Kähler if and only if its Riemann sectional curvature equals its Chern sectional curvature.
As is well known, a metric on a manifold determines a unique symmetric connection for which the metric is parallel: the Levi-Civita connection. In this paper we investigate the inverse problem: to what extent is the metric of a Riemannian manifold determined by its Levi-Civita connection? It is shown that for a generic…
Study constructs Frenet curves using semi-symmetric metric connection.
problem Understanding Frenet curves in various manifolds.
method Using semi-symmetric metric connection to construct Frenet frames and curvatures.
result Examples of semi-symmetric Frenet curves in Euclidean, Sasakian, and Kenmotsu manifolds.
Study Gauduchon connections on Kähler-like metrics in 6D solvmanifolds.
problem Investigate Hermitian metrics with Gauduchon connections having symmetries similar to Levi-Civita and Chern connections.
method Analyze 6-dimensional solvmanifolds with invariant complex structures and trivial canonical bundles. result Evidence supports two conjectures about Kähler-like conditions for different Gauduchon connections.
We address the question: how large is the family of complete metrics with nonnegative sectional curvature on S^2xR^3? We classify the connection metrics, and give several examples of non-connection metrics. We provide evidence that the family is small by proving some rigidity results for metrics more general than conne…
Classifies Riemannian manifolds with specific torsion properties.
problem Classifying Riemannian manifolds with parallel, non-twistorial torsion.
method Classifies complete simply connected Riemannian manifolds with a metric connection having parallel torsion, non-zero vectorial component, and zero twistorial component.
result Classifies complete simply connected Riemannian manifolds with the specified torsion properties.
Study invariant submanifolds in (LCS)n-manifolds with quarter symmetric metric connection.
problem Characterize invariant submanifolds in (LCS)n-manifolds.
method Investigate invariant submanifolds with respect to quarter symmetric metric connection.
result Mean curvature of invariant submanifold is equal to the mean curvature with Levi-Civita connection.
Study non-symmetric non-metric connections on Kenmotsu manifolds.
problem Properties of Kenmotsu manifolds with non-symmetric non-metric connections.
method Investigate curvature properties and irregularity of Kenmotsu manifolds.
result Kenmotsu manifolds with non-symmetric non-metric connections are irregular.
Study on curvature properties of N(κ)-contact metric manifolds with generalized Tanaka-Webster connection.
problem Curvature properties of N(κ)-contact metric manifolds.
method Analysis using generalized Tanaka-Webster connection.
result If a N(κ)-contact metric manifold with generalized Tanaka-Webster connection is K-contact, it is a generalized Sasakian space form.
Study classifies Einstein-Yang-Mills spaces in 4D symmetric spaces.
problem Classifying Lorentzian symmetric spaces with Einstein-Yang-Mills properties.
method Classification based on invariant metric connections and diagonal metrics.
result Four-dimensional symmetric spaces with nontrivial isotropy groups are classified.
Characterizes Kähler-Berwald metrics on complex manifolds.
problem Identifying Kähler-Berwald metrics among strongly convex complex Finsler metrics.
method Geometric characterization using Cartan and Chern-Finsler connections.
result Characterizes Kähler-Berwald metrics in terms of parallelism of the canonical complex structure.