Lorentzian LCS spaces are equivalent to Generalized Robertson-Walker spaces.
problem Identifying equivalent space-time structures.
method Direct demonstration of equivalence between LCS and GRW spaces.
result Lorentzian LCS spaces are equivalent to Generalized Robertson-Walker spaces.
Characterizes concircular helices in space forms and ruled hypersurfaces.
problem Understanding concircular hypersurfaces and helices in space forms.
method Characterization through differential equations and ruled hypersurfaces.
result Concircular helices are geodesics of concircular surfaces.
Characterizes concircular helices and surfaces in 3D space.
problem Understanding concircular helices and surfaces in Euclidean 3-space.
method Characterization through differential equations and ruled surfaces.
result Characterizes concircular helices and surfaces in 3D space.
The paper studies geodesic circles and concircular transformations in Finsler geometry.
problem Characterizing and understanding concircular transformations in Finsler geometry.
method Applying Lie derivatives and the Cartan Y-connection to study geodesic circles and concircular transformations. result Characterization of concircular vector fields and conditions for conformal and concircular transformations.
Study investigates concircular curvature on warped products.
problem Effects of concircular flatness and symmetry on fibre and base manifolds.
method Investigated concircular flat and symmetric warped product manifolds, considered divergence free curvature tensor.
result Results applied to generalized Robertson-Walker and static space-times.
The aim of the present paper is to investigate intrinsically the notion of a concircular π-vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the concept of a concurrent vector field in Finsler geometry. Some properties of concircular π-vector fie…
The paper characterizes Riemannian manifolds using concircular vector fields and a connecting function.
problem Characterizing Riemannian manifolds using concircular vector fields.
method Introducing a connecting function that links concircular vector fields to potential functions.
result The connecting function is crucial for characterizing n-sphere and Euclidean space. The object of this paper is to obtain the concircular curvature tensor of the semi symmetric non-metric connection on the Weyl manifold and to give a necessary and sufficient condition for a semi symmetric non-metric connection to be S-concircular.
The study examines perfect fluid spacetimes and their properties.
problem Characterizing properties of perfect fluid spacetimes with concircular vector fields.
method Analyzing the conformal curvature tensor, state equation, and solitons in perfect fluid spacetimes.
result Perfect fluid spacetimes with concircular vector fields have specific properties related to the state equation and solitons.
Study geodesic mappings and concircular fields in pseudo-Riemannian manifolds.
problem Characterize geodesic mappings and concircular fields in pseudo-Riemannian manifolds.
method Analyze geodesic mappings and concircular fields on Vn(K)-spaces, proving properties of the set of solutions. result The set of solutions of geodesic mappings on Vn(K)-spaces forms a special Jordan algebra, and the set of solutions generated by consircular fields is an ideal of this algebra. The pullback approach to global Finsler geometry is adopted. Three classes of recurrence in Finsler geometry are introduced and investigated: simple recurrence, Ricci recurrence and concircular recurrence. Each of these classes consists of four types of recurrence. The interrelationships between the different types of …
The paper examines flatness conditions on normal metric contact pairs and proves properties of Einstein manifolds.
problem The study of flatness conditions on normal metric contact pairs.
method Analysis of conformal, concircular, and quasi-conformal curvature tensors.
result Normal metric contact pair manifolds with flat conformal, concircular, and quasi-conformal curvature tensors are Einstein manifolds with specific scalar and sectional curvatures.
The paper characterizes solitons and estimates scalar curvature.
problem Characterizing and estimating scalar curvature of generalized Ricci-Yamabe solitons.
method Characterization and estimation of scalar curvature through soliton properties.
result Conditions for scalar curvature to be constant and estimation of Ricci curvature.
Study of CR-submanifolds in various Lorentzian manifolds.
problem Exploring CR-submanifolds in different Lorentzian structures.
method Analyzing properties and results of CR-submanifolds in LCS, LP-cosymplectic, S, and GKM manifolds.
result Obtained results on totally umbilical and geodesic CR-submanifolds.
Classification of Finslerian spaces with nontrivial concircular transformations.
problem Classifying Finslerian spaces with nontrivial concircular transformations.
method Proving the existence of at most two critical points in a conformal circle-preserving transformation and presenting a diffeomorphism classification based on these critical points.
result Presented a diffeomorphism classification of Finslerian manifolds that admit nontrivial conformal circle-preserving transformations.
Study on Einstein solitons with specific vector fields and their properties.
problem Characterizing Einstein solitons with gradient, solenoidal, or concircular vector fields.
method Explicitly express the function λ by gradient vector field V and deduce geometric properties under certain curvature conditions.
result Explicit expressions for λ and geometric properties of Einstein solitons.
It is proved that every concircularly recurrent manifold must be necessarily a recurrent manifold.
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. Study on solitons in Kenmotsu statistical manifolds and submanifolds.
problem Investigating solitons in Kenmotsu statistical manifolds and their submanifolds.
method Examined statistical solitons and Yamabe solitons, studied curvature properties, and analyzed submanifolds with concircular and concurrent vector fields.
result Discussed the behavior of almost quasi-Yamabe solitons on submanifolds of Kenmotsu statistical manifolds.
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 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.
Here, by extending the definition of circle to Finsler geometry, we show that, every circle-preserving local diffeomorphism is conformal. This result implies that in Finsler geometry, the definition of concircular change of metrics, a priori, does not require the conformal assumption.
The purpose of this paper is to classify α-para Kenmotsu manifolds M3 such that the projection of the image of concircular curvature tensor L in one-dimensional linear subspace of Tp(M3) generated by ξp is zero.
The paper characterizes warped product submanifolds in LCS-manifolds.
problem Characterizing warped product submanifolds in LCS-manifolds.
method Analyzing contact CR-warped product and pseudo-slant submanifolds, and constructing examples.
result There do not exist any proper warped product bi-slant submanifolds of LCS-manifolds.
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 study examines Ricci solitons and curvature inheritance on Robinson-Trautman spacetimes.
problem Investigating Ricci solitons and curvature inheritance in Robinson-Trautman spacetimes.
method Analyzing the existence of Ricci solitons and curvature inheritance properties on Robinson-Trautman spacetimes.
result Robinson-Trautman spacetimes admit various types of Ricci solitons and curvature inheritance.
It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description is proved. A formal notion of 'spin' force is discovered as a by-product of the v…
Characterizes a specific type of spacetime using vector fields.
problem Classifying a specific type of spacetime.
method Using vector fields to characterize 1+n doubly twisted spacetimes.
result Simple classification of 1+n doubly-twisted spacetimes.
We prove theorems about the Ricci and the Weyl tensors on generalized Robertson-Walker space-times of dimension n≥3. In particular, we show that the concircular vector introduced by Chen decomposes the Ricci tensor as a perfect fluid term plus a term linear in the contracted Weyl tensor. The Weyl tensor is harmoni…
A generalized Robertson-Walker spacetime is the warped product with base an open interval of the real line endowed with the opposite of its metric and base any Riemannian manifold. The family of generalized Robertson-Walker spacetimes widely extends the one of classical Robertson-Walker spacetimes. In this article we p…
The Eisenhart problem of finding parallel tensors treated already in the framework of quasi-constant curvature manifolds in \cite{x:j} is reconsidered for the symmetric case and the result is interpreted in terms of Ricci solitons. If the generator of the manifold provides a Ricci soliton then this is i) expanding on p…
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 …
Study on generalized quasi-Einstein structures in contact geometry.
problem Characterizing and understanding generalized quasi-Einstein structures in contact geometry.
method Investigation of properties, existence, and characterizations of generalized quasi-Einstein normal metric contact pair manifolds.
result Normal metric contact pair manifolds with generalized quasi-constant curvature are generalized quasi-Einstein manifolds.
Conformally quasi-recurrent (CQR)_n pseudo-Riemannian manifolds are investigated, and several new results are obtained. It is shown that the Ricci tensor and the gradient of the fundamental vector are Weyl compatible tensors (the notion was introduced recently by the authors and applies to significative space-times), (…
Discrete conjugate systems are quadrilateral nets with all planar faces. Discrete orthogonal systems are defined by the additional property of all faces being concircular. Their geometric properties allow one to consider them as proper discretization of conjugate, resp. orthogonal coordinate systems of classical differ…
In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein's equation. First, we study the geometry of sequential warped products and obtain covariant derivatives, curvature tensor, Ricci curvature and scalar curvature formulas. …
Study on generalized ξ-parallel maps in Riemannian geometry.
problem Characterizing and understanding generalized ξ-parallel maps.
method Defined energy functional, derived first variation formula, and Euler-Lagrange equation.
result Established fundamental properties and relationships with harmonic and biharmonic maps.
The study proves triviality and rigidity results for Ricci solitons and estimates their conjugate radius.
problem Understanding the properties and behavior of Ricci solitons.
method Analytical proofs and estimates for various types of Ricci solitons.
result Upper bounds and estimates for conjugate radius of Ricci solitons.
Compact Finslerian manifolds don't admit non-trivial circle-preserving transformations.
problem Characterizing Finslerian manifolds without circle-preserving transformations.
method Analyzing critical points of conformal transformations to prove manifold rigidity.
result Compact Finslerian manifolds are Riemannian and conformally diffeomorphic to standard spheres, Euclidean spaces, or hyperbolic spaces.
The study characterizes Euclidean submanifolds with a conformal canonical vector field.
problem Characterizing Euclidean submanifolds with a specific vector field property.
method Investigating properties of the canonical vector field and its conformal nature.
result Characterization of Euclidean submanifolds with conformal canonical vector fields.
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. 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.
Defines compatibility between Riemannian and Jacobi structures.
problem Understanding the relationship between Riemannian and Jacobi structures.
method Introducing a notion of compatibility and proving results for specific examples.
result Establishes compatibility for Poisson, contact, and locally conformally symplectic structures.
The paper introduces new structures for left-symmetric algebroids.
problem Developing new mathematical structures for left-symmetric algebroids.
method Introducing Koszul-Vinberg-Nijenhuis structures and related concepts.
result Koszul-Vinberg-Nijenhuis structures provide a hierarchy of structures.
Defines compatibility between Riemannian and Jacobi structures.
problem Understanding compatibility between Riemannian and Jacobi structures.
method Introducing a notion of compatibility and proving it for specific structures.
result Fundamental examples of Jacobi structures lead to known structures like Riemann-Poisson, Kenmotsu, and locally conformally Kähler.
Extending Jacobi and Riemannian compatibility to Lie algebroids.
problem Generalizing compatibility between Jacobi and Riemannian structures.
method Generalizing previous work on fundamental examples to Lie algebroids.
result Compatibility results for Lie algebroids.
Study projective and direct limits of Banach structures with connections to G-structures.
problem Understanding connections between Banach structures and G-structures. method Endow projective and direct limits with Fréchet or convenient structures and study connections.
result Illustrated examples demonstrate the study of projective and direct limits.
Defines structure constants for specific geometric structures on Lie groups.
problem No specific problem stated; focuses on defining structure constants.
method Not explicitly detailed in the abstract.
result Defines structure constants for almost complex, almost symplectic, and Riemannian structures on a local Lie group.