Investigates curvature properties of Robinson-Trautman metric.
problem Examines curvature characteristics of Robinson-Trautman metric.
method Analyzes various pseudosymmetric structures and properties of the metric.
result The metric exhibits multiple curvature properties including Roter type, 2-quasi-Einstein, and Riemann compatible.
The paper examines curvature properties of a specific magnetic spacetime metric.
problem Investigating the geometric properties of Melvin magnetic spacetime metric.
method Analyzing a Melvin type static, cylindrically symmetric spacetime metric in Weyl form, considering curvature conditions and tensor properties.
result The Melvin magnetic metric is pseudosymmetric and satisfies the Roter type condition.
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 geometric properties of Bardeen black hole spacetime.
problem Examines curvature properties of Bardeen black hole spacetime.
method Analyzes pseudosymmetry, pseudosymmetric Weyl curvature, and recurrent structures.
result Bardeen spacetime is a manifold of pseudosymmetry Weyl curvature and satisfies special recurrent like structure.
The paper classifies certain N(κ)-contact metric manifolds under specific conditions.
problem Investigating properties of N(κ)-contact metric manifolds. method Analyzing manifolds under specific curvature conditions.
result Weyl-pseudosymmetric N(κ)-contact metric manifolds are either locally isometric to En+1(0)imesSn(4) or η-Einstein. 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.
The paper examines Ricci solitons on specific types of (LCS)n-manifolds.
problem Investigating Ricci solitons on (LCS)n-manifolds. method Analyzing various types of Ricci pseudosymmetric (LCS)n-manifolds. result Conditions for Ricci solitons on specific (LCS)n-manifolds. The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.
problem Characterizing pseudosymmetric spacetimes as perfect fluids.
method Analyzes generalized Robertson-Walker spacetimes, conformally flat spacetimes, and dust fluids.
result Conditions for pseudosymmetric spacetimes to be perfect fluids are established.
Definition of (Ta,Tb)-pseudosymmetric semi-Riemannian manifold is given. (Ta,Tb)-pseudosy mmetric (N(k),ξ)-semi-Riemannian manifolds are classified. Some results for Ta-pseudosymmetric (N(k),ξ)-semi-Riemannian manifolds are obtained. $({\cal T}_{a},{\cal T}_{b…
In the literature, there are two different notions of pseudosymmetric manifolds, one by Chaki [7] and other by Deszcz [16], and there are many papers related to these notions. The object of the present paper is to deduce necessary and sufficient conditions for a Chaki pseudosymmetric [7] (resp. pseudo Ricci symmetric […
The paper characterizes warped product manifolds under pseudosymmetric conditions.
problem Characterizing warped product manifolds under pseudosymmetric conditions.
method Examining the pseudosymmetric type condition \( R \cdot R = L_1 Q(g,R) + L_2 Q(S,R) \) and evaluating the characterization theorem.
result Necessary and sufficient conditions for various pseudosymmetric types in warped product manifolds.
The paper classifies a specific type of contact metric manifolds.
problem Classifying (κ,μ)-contact metric manifolds. method Using Ricci-generalized pseudosymmetric properties defined by Deszcz.
result Classification of (κ,μ)-contact metric manifolds. The aim of this paper is to present the first examples of compact, simply connected holomorphically pseudosymmetric Kahler manifolds.
The aim of this paper is to present examples of Kahler holomorphically pseudosymmetric metrics on the projective space CP^n.
For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct exampl…
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.
Geodesic mappings found in a specific type of warped product manifolds.
problem Characterizing geodesic mappings in a particular class of Roter spaces.
method Identifying a specific class of Roter type warped product manifolds and proving geodesic mappings onto another Roter type warped product manifold.
result Both geodesically related manifolds are pseudosymmetric of constant type.
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 …
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.
Study properties of hyperbolic Yamabe solitons in submanifolds.
problem Characterize and understand hyperbolic Yamabe solitons in submanifolds.
method Define hyperbolic Yamabe flow, prove properties, and classify solitons.
result Prove that hyperbolic Yamabe solitons are pseudosymmetric or metallic shaped.
The paper examines curvature properties of Vaidya metric, a generalization of Schwarzschild solution.
problem Investigating curvature properties of Vaidya metric.
method Analyzing Vaidya metric under different curvature conditions and comparing with Ludwig-Edgar pure radiation metric.
result Vaidya metric exhibits various curvature properties including pseudosymmetric type conditions and is Ricci simple.
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.
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. Extends Weyl geometry from conformal to Weyl manifolds using ambient metrics.
problem Generalizing ambient constructions to Weyl manifolds.
method Introduces Weyl-ambient metric and Weyl-Fefferman-Graham gauge; shows Weyl-ambient space induces Weyl geometry; defines Weyl-connection and Weyl structure.
result Weyl-ambient construction for Weyl manifolds provides a well-defined initial value problem.
Study finds holonomy algebras for Lorentzian Weyl spin manifolds with specific spinors.
problem Characterizing Lorentzian Weyl spin manifolds with weighted parallel spinors.
method Analyzing holonomy algebras and introducing special coordinates.
result Local forms and examples of Lorentzian Weyl spin manifolds with weighted parallel spinors.
The paper examines geometric properties of a specific black hole spacetime.
problem Curvature properties of a Hayward black hole spacetime.
method Analyzes the curvature properties of Hayward black hole spacetime using Einstein field equations.
result The Hayward black hole spacetime is an Einstein manifold and exhibits various types of pseudosymmetry.
The paper studies automorphisms of Weyl manifolds and constructs modified contact Weyl diffeomorphisms.
problem Analyzing the automorphisms of Weyl manifolds associated with symplectic structures.
method Investigates the automorphisms of Weyl manifolds corresponding to Poincaré-Cartan classes and constructs modified contact Weyl diffeomorphisms.
result Construction of modified contact Weyl diffeomorphisms and analysis of automorphisms of Weyl manifolds.
The study explores Einstein-Weyl structures on specific types of manifolds.
problem Investigating properties of Einstein-Weyl structures on almost cosymplectic manifolds.
method Analyzing conditions for Einstein-Weyl structures on (κ,μ)-manifolds, three-dimensional compact manifolds, and K-cosymplectic manifolds. result Conditions for manifolds to be Einstein, cosymplectic, or Ricc-flat.
The paper studies Weyl-minimal surfaces and their adjunction inequality.
problem Investigating Weyl-minimal surfaces in conformal manifolds.
method Analyzes Weyl-minimal surfaces and their relation to Eells-Salamon curves.
result Branched Weyl-minimal surfaces satisfy the adjunction inequality.
Holonomy of Weyl connections in Lorentzian space classified.
problem Classifying holonomy algebras of Weyl connections in Lorentzian signature.
method Classification through construction of examples of Weyl connections with all possible holonomy algebras.
result Examples of Weyl connections with all possible holonomy algebras constructed.
This thesis explores Weyl geometry and quantum anomalies in holography and gauge theories.
problem Understanding Weyl geometry and quantum anomalies in holographic and gauge theories.
method Generalized Weyl-covariant holography, Lie algebroid encoding of BRST complex, and Lie algebroid cohomology.
result Weyl obstruction tensors are used to compute Weyl anomalies and provide geometric insights into quantum anomalies.
New Clifford-Weyl structures defined on conformal manifolds.
problem Understanding the geometry of even Clifford structures on conformal manifolds.
method Introduced Clifford-Weyl structures and showed conditions for their closure.
result Weyl structures are closed except in low-dimensional cases.
Motivated by the study of Weyl structures on conformal manifolds admitting parallel weightless forms, we define the notion of conformal product of conformal structures and study its basic properties. We obtain a classification of Weyl manifolds carrying parallel forms, and we use it to investigate the holonomy of the a…
We determine the space of algebraic pseudo-Hermitian Kähler-Weyl curvature tensors and the space of para-Hermitian Kähler-Weyl curvature tensors in dimension 4 and show that every algebraic possibility is geometrically realizable. We establish the Gray identity for pseudo-Hermitian Weyl manifolds and for para-Hermitian…
The abstract discusses transformations on statistical and semi-Weyl manifolds with torsion.
problem Invariance and structure preservation under conformal-projective transformations.
method Proof of invariance and preservation of structures under conformal-projective transformations.
result Semi-Weyl and statistical structures with torsion are invariant under conformal-projective transformations.
Study pseudo-harmonic maps on Weyl manifolds.
problem Characterize conditions for a Hermitian-Weyl manifold's complex structure to be a pseudo-harmonic map.
method Investigate geometric conditions for pseudo-harmonic maps in the context of Hermitian-Weyl manifolds.
result Find conditions for the complex structure to be a pseudo-harmonic map under specific dimensions or conformal structures.
A Riemannian manifold is called Weyl homogeneous, if its Weyl tensors at any two points are "the same", up to a positive multiple. A Weyl homogeneous manifold is modeled on a homogeneous space M0, if its Weyl tensor at every point is "the same" as the Weyl tensor of M0, up to a positive multiple. We prove that a …
This is a survey on quaternion Hermitian Weyl (locally conformally quaternion Kähler) and hyperhermitian Weyl (locally conformally hyperkähler) manifolds. These geometries appear by requesting the compatibility of some quaternion Hermitian or hyperhermitian structure with a Weyl structure. The motivation for such a stu…
Weak harmonic Weyl metrics found on all 4D closed manifolds.
problem Finding canonical metrics on 4D closed manifolds.
method Critical points of a quadratic functional involving the divergence of the Weyl tensor.
result Every 4D closed manifold admits a unique weak harmonic Weyl metric.
We show that the Weyl structure of an almost-Hermitian Weyl manifold of dimension at least 6 is trivial if the associated curvature operator satisfies the Kaehler identity. Similarly if the curvature of an almost para-Hermitian Weyl manifold of dimension at least 6 satisfies the para-Kaehler identity, then the Weyl str…
Investigates Schouten-Weyl tensor on 3D Lie groups with specific metrics.
problem Analyzing the Schouten-Weyl tensor on 3D Lie groups with special metrics.
method Examines left-invariant Lorentzian metrics and investigates harmonicity of the tensor.
result Identifies specific Lie groups with zero Schouten-Weyl tensor.
New manifold structures on Weyl group orbit spaces proven.
problem Constructing generalized Frobenius manifold structures.
method Construction on orbit spaces of affine Weyl groups.
result Monodromy groups are parabolic subgroups.
We classify the possible local holonomy groups of Weyl connections. The Berger-Simons theorem and the Merkulov-Schwachhöfer classification of holonomy groups of irreducible torsion-free connections leaves us with the remaining case, where the Weyl connection D is reducible and non-closed. In this case, it was shown b…
In this paper we study the 3-dimensional (ε)-para Sasakian manifolds. We obtain an necessary and sufficient condition for an (ε)-para Sasakian 3 -manifold to be an indefinite space form. We show that a Ricci-semi-symmetric (ε)-para Sasakian 3 -manifold is an indefinite space form…
Study complete gradient Ricci solitons with zero radial Weyl curvature.
problem Characterize complete gradient Ricci solitons with specific curvature properties.
method Classify complete gradient Ricci solitons with zero radial Weyl curvature for dimensions n≥4. result Completely classified complete gradient Ricci solitons with zero radial Weyl curvature.
Study pinched self-dual Weyl curvature in compact 4-manifolds.
problem Analyzing compact 4-manifolds with specific curvature properties.
method Examining harmonic self-dual Weyl curvature under pinching conditions.
result Characterized compact 4-manifolds with pinched self-dual Weyl curvature.
We work in both the complex and in the para-complex categories and examine (para)-Kähler Weyl structures in both the geometric and in the algebraic settings. The higher dimensional setting is quite restrictive. We show that any (para)-Kaehler Weyl algebraic curvature tensor is in fact Riemannian in dimension at least 6…
We show any Weyl curvature model can be geometrically realized by a Weyl manifold