scholarly journals On Lorentzian spaces of constant sectional curvature

2018 ◽  
Vol 103 (117) ◽  
pp. 7-15
Author(s):  
Vladica Andrejic
Keyword(s):  
Sectional Curvature ◽  
Curvature Tensor ◽  
Jacobi Operator ◽  
Constant Sectional Curvature ◽  
Duality Principle ◽  
Lorentzian Manifolds ◽  
Algebraic Curvature Tensor ◽  
Algebraic Curvature ◽  
Curvature Tensors

We investigate Osserman-like conditions for Lorentzian curvature tensors that imply constant sectional curvature. It is known that Osserman (moreover zwei-stein) Lorentzian manifolds have constant sectional curvature. We prove that some generalizations of the Rakic duality principle (Lorentzian totally Jacobi-dual or four-dimensional Lorentzian Jacobi-dual) imply constant sectional curvature. Moreover, any four-dimensional Jacobi-dual algebraic curvature tensor such that the Jacobi operator for some nonnull vector is diagonalizable, is Osserman. Additionally, any Lorentzian algebraic curvature tensor such that the reduced Jacobi operator for all nonnull vectors has a single eigenvalue has a constant sectional curvature.

scholarly journals On quasi-Clifford Osserman curvature tensors

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1241-1247
Author(s):  
Vladica Andrejic ◽  
Katarina Lukic
Keyword(s):  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Duality Principle ◽  
Algebraic Curvature ◽  
Curvature Tensors

We consider pseudo-Riemannian generalizations of Osserman, Clifford, and the duality principle properties for algebraic curvature tensors and investigate relations between them. We introduce quasi- Clifford curvature tensors using a generalized Clifford family and show that they are Osserman. This allows us to discover an Osserman curvature tensor that does not satisfy the duality principle. We give some necessary and some sufficient conditions for the total duality principle.

scholarly journals Indefinite Almost Paracontact Metric Manifolds

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Mukut Mani Tripathi ◽  
Erol Kılıç ◽  
Selcen Yüksel Perktaş ◽  
Sadık Keleş
Keyword(s):  
Riemannian Manifold ◽  
Sectional Curvature ◽  
Curvature Tensor ◽  
Ricci Tensor ◽  
Sasakian Manifold ◽  
Constant Sectional Curvature ◽  
Sasakian Manifolds ◽  
Sasakian Structure

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 semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it cannot admit an (ε)-para Sasakian structure. We show that, for an (ε)-para Sasakian manifold, the conditions of being symmetric, semi-symmetric, or of constant sectional curvature are all identical. It is shown that a symmetric spacelike (resp., timelike) (ε)-para Sasakian manifoldMnis locally isometric to a pseudohyperbolic spaceHνn(1)(resp., pseudosphereSνn(1)). At last, it is proved that for an (ε)-para Sasakian manifold the conditions of being Ricci-semi-symmetric, Ricci-symmetric, and Einstein are all identical.

scholarly journals The duality principle for Osserman algebraic curvature tensors

2016 ◽  
Vol 504 ◽  
pp. 574-580
Author(s):  
Y. Nikolayevsky ◽  
Z. Rakić
Keyword(s):  
Duality Principle ◽  
Algebraic Curvature ◽  
Curvature Tensors

scholarly journals GEOMETRIC REALIZATIONS OF KAEHLER AND OF PARA-KAEHLER CURVATURE MODELS

2010 ◽  
Vol 07 (03) ◽  
pp. 505-515 ◽  
Author(s):  
M. BROZOS-VÁZQUEZ ◽  
P. GILKEY ◽  
E. MERINO
Keyword(s):  
Scalar Curvature ◽  
Curvature Tensor ◽  
Constant Scalar Curvature ◽  
Kaehler Manifold ◽  
Algebraic Curvature Tensor ◽  
Algebraic Curvature

We show that every Kaehler algebraic curvature tensor is geometrically realizable by a Kaehler manifold of constant scalar curvature. We also show that every para-Kaehler algebraic curvature tensor is geometrically realizable by a para-Kaehler manifold of constant scalar curvature.

scholarly journals On pseudo H-symmetric Lorentzian manifolds with applications to relativity

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3287-3297
Author(s):  
Uday De ◽  
Young Suh ◽  
Sudhakar Chaubey ◽  
Sameh Shenawy
Keyword(s):  
Curvature Tensor ◽  
Lorentzian Manifold ◽  
Lorentzian Manifolds ◽  
Lorentzian Metric ◽  
Projective Curvature ◽  
Almost Product Manifold ◽  
New Type ◽  
Curvature Tensors ◽  
Fluid Spacetimes

In this paper, we introduce a new type of curvature tensor named H-curvature tensor of type (1, 3) which is a linear combination of conformal and projective curvature tensors. First we deduce some basic geometric properties of H-curvature tensor. It is shown that a H-flat Lorentzian manifold is an almost product manifold. Then we study pseudo H-symmetric manifolds (PHS)n (n > 3) which recovers some known structures on Lorentzian manifolds. Also, we provide several interesting results. Among others, we prove that if an Einstein (PHS)n is a pseudosymmetric (PS)n, then the scalar curvature of the manifold vanishes and conversely. Moreover, we deal with pseudo H-symmetric perfect fluid spacetimes and obtain several interesting results. Also, we present some results of the spacetime satisfying divergence free H-curvature tensor. Finally, we construct a non-trivial Lorentzian metric of (PHS)4.

scholarly journals The nonexistence of rank4IP tensors in signature(1,3)

2002 ◽  
Vol 31 (5) ◽  
pp. 259-269
Author(s):  
Kelly Jeanne Pearson ◽  
Tan Zhang
Keyword(s):  
Vector Space ◽  
Curvature Tensor ◽  
Bilinear Form ◽  
Symmetric Operator ◽  
Symmetric Bilinear Form ◽  
Real Vector Space ◽  
Real Vector ◽  
Algebraic Curvature Tensor ◽  
Algebraic Curvature

LetVbe a real vector space of dimension4with a nondegenerate symmetric bilinear form of signature(1,3). We show that there exists no algebraic curvature tensorRonVso that its associated skew-symmetric operatorR(⋅)has rank4and constant eigenvalues on the Grassmannian of nondegenerate2-planes inV.

scholarly journals Quasi-special Osserman manifolds

Filomat ◽  
2014 ◽  
Vol 28 (3) ◽  
pp. 623-633 ◽  
Author(s):  
Vladica Andrejic
Keyword(s):  
Curvature Tensor ◽  
Jacobi Operator ◽  
Duality Principle ◽  
Insight Into

In this paper we deal with a pseudo-Riemannian Osserman curvature tensor whose reduced Jacobi operator is diagonalizable with exactly two distinct eigenvalues. The main result gives new insight into the theory of the duality principle for pseudo-Riemannian Osserman manifolds. We concern with special Osserman curvature tensor and propose new ways to exclude some additional duality principle conditions from its definition.

H-curvature tensors on IK-normal complex contact metric manifolds

2018 ◽  
Vol 15 (12) ◽  
pp. 1850205 ◽  
Author(s):  
Aysel Turgut Vanli ◽  
Inan Unal
Keyword(s):  
Sectional Curvature ◽  
Constant Sectional Curvature ◽  
Theoretical Physics ◽  
Contact Metric Manifold ◽  
Contact Manifolds ◽  
Normal Complex ◽  
Contact Metric Manifolds ◽  
Curvature Tensors

IK-normal complex contact metric manifolds have some important properties. There are several applications of this kind of contact manifolds in theoretical physics. In this paper, we studied on [Formula: see text]-curvature tensors for IK-normal complex contact metric manifolds. We have shown that there is no IK-normal complex contact metric manifold with constant sectional curvature and an IK-normal complex contact metric manifold is not Ricci semi-symmetric.

Homogeneous Einstein Finsler Metrics on -dimensional Spheres

2018 ◽  
Vol 62 (3) ◽  
pp. 509-523
Author(s):  
Libing Huang ◽  
Xiaohuan Mo
Keyword(s):  
Sectional Curvature ◽  
Ricci Curvature ◽  
Einstein Metrics ◽  
Constant Sectional Curvature ◽  
Einstein Metric ◽  
Finsler Metrics ◽  
Dimensional Sphere ◽  
Order Ordinary Differential Equation ◽  
Canonical Metric ◽  
Homogeneous Einstein Metrics

AbstractIn this paper, we study a class of homogeneous Finsler metrics of vanishing $S$-curvature on a $(4n+3)$-dimensional sphere. We find a second order ordinary differential equation that characterizes Einstein metrics with constant Ricci curvature $1$ in this class. Using this equation we show that there are infinitely many homogeneous Einstein metrics on $S^{4n+3}$ of constant Ricci curvature $1$ and vanishing $S$-curvature. They contain the canonical metric on $S^{4n+3}$ of constant sectional curvature $1$ and the Einstein metric of non-constant sectional curvature given by Jensen in 1973.

Sign in / Sign up

Export Citation Format

Share Document