Study examines moduli spaces of Type~A connections on surfaces with Ricci tensor properties.
problem Characterize moduli spaces of Type~A connections on surfaces with specific Ricci tensor signatures.
method Analyzed connections on surfaces with torsion and non-singular symmetric Ricci tensor, considering different signatures.
result Moduli spaces are smooth if Ricci tensor signature is (1,1) or (0,2), and have orbifold singularities if signature is (2,0).
Characterizes Lorentzian manifolds with semi-symmetric metric connections.
problem Characterizing Lorentzian manifolds with specific metric connections.
method Analyzing semi-symmetric metric connections with vanishing curvature and recurrent torsion.
result Establishes conditions for perfect fluid and generalized Robertson-Walker spacetimes.
Study on new connections in para-Sasakian manifolds.
problem Exploring new generalized symmetric metric connections in para-Sasakian manifolds.
method Identified and utilized generalized symmetric connections of type (α,β) on Lorentzian para-Sasakian manifolds.
result Obtained new results involving curvature and Ricci tensors on para-Sasakian manifolds.
We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric.
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.
Some known results on torsionfree connections with skew-symmetric Ricci tensor on surfaces are extended to connections with torsion, and Wong's canonical coordinate form of such connections is simplified.
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.
We determine the isomorphism classes of symmetric symplectic manifolds of dimension at least 4 which are connected, simply-connected and have a curvature tensor which has only one non-vanishing irreducible component -- the Ricci tensor.
The paper studies geodesic mappings in special Riemannian manifolds.
problem Investigating geodesic mappings in specific Riemannian manifolds.
method Proof of geodesic mappings properties and new results on geodesic mappings of various Riemannian manifolds.
result New results on geodesic mappings of quasi Einstein, Ricci recurrent, and Ricci symmetric manifolds.
The paper examines *-Ricci tensor properties on Sasakian manifolds.
problem Analyzing *-Ricci tensor on Sasakian manifolds.
method Examining φ-confomally flat and confomally flat *-η-Einstein Sasakian manifolds, *-Ricci symmetric condition, and *-Ricci soliton.
result Investigates properties of *-Ricci tensor on Sasakian manifolds.
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.
Defines semi-symmetric metric connections on differential forms.
problem Analyzing connections on differential forms.
method Defined and studied semi-symmetric metric connections, computed their curvature and Ricci tensors, and analyzed Lie derivatives.
result Derived Gauss-Codazzi-Ricci equations and properties of canonical, Schouten, and Vrancreanu connections.
Defines a tensor related to Q-curvature on manifolds.
problem Understanding Q-curvature and its applications.
method Defines a symmetric 2-tensor J-tensor associated to Q-curvature.
result Establishes a relation between J-tensor and Q-curvature, akin to Ricci tensor and scalar curvature.
We introduce a new kind of Riemannian manifold that includes weakly-, pseudo- and pseudo projective- Ricci symmetric manifolds. The manifold is defined through a generalization of the so called Z tensor; it is named "weakly Z symmetric" and denoted by (WZS)_n. If the Z tensor is singular we give conditions for the exis…
Study parallel tensors on affine surfaces to characterize Ricci recurrence.
problem Characterizing affine surfaces with specific geometric properties.
method Analyzing parallel trace-free tensors and Ricci recurrence.
result Existence of parallel tensors is linked to Ricci recurrence.
New pseudo-Kähler Einstein spaces found with special almost complex structures.
problem Identifying new pseudo-Kähler Einstein spaces with special almost complex structures.
method Examining 4-symmetric symplectic spaces with compatible almost complex structures.
result Found pseudo-Kähler Einstein spaces with an integrable and non-integrable pair of compatible almost complex structures.
The Eisenhart problem of finding parallel tensors is solved for the symmetric case in the regular f-Kenmotsu framework. On this way, the Olszack-Rosca example of Einstein manifolds provided by f-Kenmotsu manifolds via locally symmetric Ricci tensors is recovered as well as a case of Killing vector fields. Some othe…
New generalized symmetric connections defined for Kenmotsu manifolds.
problem Characterizing new connections in Kenmotsu manifolds.
method Defined and analyzed new generalized symmetric connections (α,β) on Kenmotsu manifolds. result Provided results involving curvature tensors for Kenmotsu manifolds.
Study on moduli spaces of Type~B surfaces with torsion.
problem Examining moduli spaces of locally homogeneous surfaces with torsion.
method Analyzing symmetric Ricci tensor and affine Killing vector fields.
result Determined the space of affine Killing vector fields.
Study of η-Ricci solitons on Kenmotsu 3-manifolds.
problem Exploring η-Ricci solitons on Kenmotsu 3-manifolds. method Examined various types of η-Ricci solitons on Kenmotsu 3-manifolds, including those with specific curvature conditions. result Existence of proper η-Ricci solitons on Kenmotsu 3-manifolds. We examine questions of geometric realizability for algebraic structures which arise naturally in affine and Riemannian geometry. Suppose given an algebraic curvature operator R at a point P of a manifold M and suppose given a real analytic (resp. C-k for finite k at least 2) pseudo-Riemannian metric on M defined near …
Study of η-Ricci solitons on (ε)-almost paracontact metric manifolds.
problem Investigating η-Ricci solitons on specific types of manifolds. method Analyzing η-Ricci solitons under different conditions and tensor fields. result Obtained results for η-Ricci solitons on (ε)-almost paracontact metric manifolds. In this paper we study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Schouten tensor on compact Riemannian manifolds with boundary. We prove its solvability and the compactness of the solution set, provided the Ricci tensor is non-negative definite.
Study on quasi-Einstein and generalized quasi-Einstein warped products with a semi-symmetric non-metric connection.
problem Exploring properties and obstructions of quasi-Einstein and generalized quasi-Einstein warped products.
method Analyzing expressions of Ricci tensors and scalar curvatures for bases and fibres with a semi-symmetric non-metric connection.
result Some obstructions to the existence of quasi-Einstein and generalized quasi-Einstein warped products with a semi-symmetric non-metric connection.
Equivalence proven between different Ricci curvature definitions.
problem Equivalence of various Ricci curvature definitions.
method Proof of equivalence between different Ricci curvature definitions.
result Equivalence proven between several Ricci curvature definitions.
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…
Study on Ricci-like solitons on specific geometric manifolds, finding properties and conditions.
problem Characterizing Ricci-like solitons on Sasaki-like almost contact B-metric manifolds.
method Analyzing cases with specific potential fields and studying curvature conditions.
result Found conditions for the potential to have constant length and manifold to be η-Einstein. The paper explores properties of affine Szabó manifolds and their metrics.
problem Understanding the properties and metrics of affine Szabó manifolds.
method Analyzes the properties of affine Szabó manifolds and their metrics, proving necessary and sufficient conditions.
result Affine Szabó manifolds have specific properties regarding their Ricci tensor and recurrence covector.
Stability of Einstein metrics under Ricci iteration studied.
problem Stability of Einstein metrics under Ricci iteration.
method Sufficient condition based on Lichnerowicz Laplacian spectrum.
result Stability of several Einstein manifolds including symmetric spaces.
In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product R×Nn−1, or globally conformally equivalent to the Euclidean space Rn or to the round sphere Sn. In particular, we show that any comple…
The paper examines geometric properties of a unique spacetime model.
problem Investigating the geometric properties of a point-like global monopole spacetime.
method Analyzing the spacetime's pseudosymmetry structures, energy-momentum tensor, and curvature properties.
result The point-like global monopole spacetime exhibits various pseudosymmetry structures and properties.
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 equation determining whether a projective structure admits a connection in its given projective class that has skew-symmetric Ricci tensor is an overdetermined system of semi-linear partial differential equations which we call the projective Einstein-Weyl (pEW) equation. In 2-dimensions, we give local obstructions …
A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend from it. Applications to manifolds with Recurrent or Symmetric structures are discussed. The new structure of K-rec…
In this paper is considered the differential equation Ric(g)=T, where Ric(g) is the Ricci tensor of the metric g and T is a rotational symmetric tensor on R^n. A new, geometric, proof of the existence of smooth solutions of this equation, based on qualitative theory of implicitdifferential equations, is presented here.…
The paper extends results on Bach-flat solitons to new types.
problem Analyzing Bach-like tensors on complete gradient Ricci solitons.
method Extending previous results to new types of solitons.
result Results on Bach-flat solitons extended to new types.
Study spherical doubly warped spacetimes for stellar collapse and cosmology.
problem Analyzing spherically symmetric spacetimes for stellar collapse and cosmology.
method Obtained results for Weyl and Ricci tensors on general doubly warped spacetimes.
result Friedmann equations deviate from standard FRW cosmology due to electric tensor terms.
We prove the vanishing of the first Betti number on compact manifolds admitting a Weyl structure whose Ricci tensor satisfies certain positivity conditions, thus obtaining a Bochner-type vanishing theorem in Weyl geometry. We also study compact Hermitian-Weyl manifolds with non-negative symmetric part of the Ricci tens…
For a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A.…
We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally appear in relative hypersurface theory.
This paper explores Lorentzian manifolds with specific connections and their symmetries.
problem Characterizing Lorentzian manifolds with concircularly semi-symmetric metric connections.
method Investigates the properties of Lorentzian manifolds equipped with a concircularly semi-symmetric metric connection under specific conditions.
result Derives necessary and sufficient conditions for the manifold to be Einstein and proves that a perfect fluid space-time with a semi-symmetric metric P-connection is Ricci pseudo-symmetric manifold of constant type. New infinite families of flat spaces found from symmetric spaces.
problem Finding new flat homogeneous spaces.
method Starting from compact symmetric spaces, constructing infinite families of compact homogeneous spaces with invariant Bismut connections.
result Infinite families of compact homogeneous spaces with vanishing Ricci tensor.
The paper explores geometric decompositions for Ricci tensors and their applications.
problem Understanding Ricci tensors on compact Riemannian manifolds.
method Utilizes Berger-Ebin and York L2-orthogonal decompositions. result New insights into Ricci almost solitons and harmonic maps.
Study moduli spaces of 3D homogeneous manifolds with specific properties.
problem Characterize moduli spaces of oriented Type A manifolds in 3D.
method Analyze manifolds with symmetric Ricci tensor, torsion, and varying dimensions.
result Determine all symmetry groups in 3D torsion-free manifolds.
Study of curvature tensor algebra with nonstandard multiplications.
problem Understanding curvature tensor algebra structures.
method Investigates orthogonally invariant commutative nonassociative multiplications on curvature tensors.
result Characterizes curvature tensor algebras in low dimensions and proves their simplicity in higher dimensions.
Generalizes DeTurck's theorem to non-compact manifolds.
problem Uniquely determine Levi-Civita connection from Ricci curvature.
method Extends DeTurck's theorem to non-compact manifolds.
result Generalization to non-compact manifolds with finite total scalar curvature.
Study on Einstein warped spaces with specific connections and curvature properties.
problem Characterizing Einstein warped spaces with quarter symmetric connections.
method Analyzing curvature, Ricci, and scalar tensors with quarter symmetric connections.
result Proves conditions under which an Einstein warped space becomes a Riemannian product space.
Researchers find conditions for a specific curvature on Lie groups.
problem Conditions for a specific Ricci curvature on three-dimensional unimodular Lie groups.
method Provided necessary and sufficient conditions for the existence of a pair (g, c) with left-invariant Riemannian metric g and positive constant c such that Ric(g) = cT.
result Existence and uniqueness of solutions for the prescribed Ricci curvature problem on Lie groups.