Some curvature restricted geometric structures for projective curvature tensors

2018 ◽  
Vol 15 (09) ◽  
pp. 1850157 ◽  
Author(s):  
Absos Ali Shaikh ◽  
Haradhan Kundu
Keyword(s):  
Curvature Tensor ◽  
Riemannian Manifolds ◽  
Einstein Manifolds ◽  
Geometric Structures ◽  
Projective Curvature ◽  
Riemannian Case ◽  
Projective Curvature Tensor ◽  
Projective Operator ◽  
Curvature Tensors

The projective curvature tensor is an invariant under geodesic preserving transformations on semi-Riemannian manifolds. It possesses different geometric properties than other generalized curvature tensors. The main object of the present paper is to study some semisymmetric type and pseudosymmetric type curvature restricted geometric structures due to projective curvature tensor. The reduced pseudosymmetric type structures for various Walker type conditions are deduced and the existence of Venzi space is ensured. It is shown that the geometric structures formed by imposing projective operator on a (0,4)-tensor is different from that for the corresponding (1,3)-tensor. Characterization of various semisymmetric type and pseudosymmetric type curvature restricted geometric structures due to projective curvature tensor are obtained on semi-Riemannian manifolds, and it is shown that some of them reduce to Einstein manifolds for the Riemannian case. Finally, to support our theorems, four suitable examples are presented.

scholarly journals Riemannian manifolds satisfying certain conditions on pseudo-projective curvature tensor

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 721-731 ◽  
Author(s):  
Sinem Güler ◽  
Sezgin Demirbağ
Keyword(s):  
Curvature Tensor ◽  
Riemannian Manifolds ◽  
Einstein Manifold ◽  
Einstein Manifolds ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Projective Flatness

In this paper we determine some properties of pseudo-projective curvature tensor denoted by ?P on some Riemannian manifolds, especially on generalized quasi Einstein manifolds in the sense of Chaki. Firstly, we consider a pseudo-projectively Ricci semisymmetric generalized quasi Einstein manifold. After that, we study pseudo-projective flatness of this manifold. Moreover, we construct a non-trivial example for a generalized quasi Einstein manifold to prove the existence.

M-projective curvature tensor on an (LCS)2n+1-manifold

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Shanmukha ◽  
V. Venkatesha
Keyword(s):  
Curvature Tensor ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Curvature Tensors

Abstract In this paper, we study M-projective curvature tensors on an ( LCS ) 2 ⁢ n + 1 {(\mathrm{LCS})_{2n+1}} -manifold. Here we study M-projectively Ricci symmetric and M-projectively flat admitting spacetime.

scholarly journals Projective Curvature Tensor with Respect to Zamkovoy Connection in Lorentzian Para-Sasakian Manifolds

2020 ◽  
Vol 26 (3) ◽  
pp. 369-379
Author(s):  
Abhijit Mandal ◽  
Ashoke Das
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Curvature Tensors

The purpose of the present paper is to study some properties of the Projective curvature tensor with respect to Zamkovoy connection in Lorentzian Para Sasakian manifold(or,LP-Sasakian manifold)'And we have studied some results in Lorentzian Para-Sasakian manifold with the help of Zamkovoy connection and Projective curvature tensor.Also we discussed the LP-Sasakian manifold satisfying P*(ξ,U)∘W₀*=0,P*(ξ,U)∘W₂*=0 , where W₀*,W₂* and P* are W₀,W₂ and Projective curvature tensors with respect to Zamkovoy connection.

scholarly journals Generalized para-Kähler spaces in Eisenhart’s sense admitting a holomorphically projective mapping

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4001-4012
Author(s):  
Milos Petrovic
Keyword(s):  
Curvature Tensor ◽  
Product Structure ◽  
Projective Mapping ◽  
Almost Product Structure ◽  
Projective Curvature ◽  
Geometric Objects ◽  
Projective Curvature Tensor ◽  
Curvature Tensors

We relax the conditions related to the almost product structure and in such a way introduce a wider class of generalized para-K?hler spaces. Some properties of the curvature tensors as well as those of the corresponding Ricci tensors of these spaces are pointed out. We consider holomorphically projective mappings between generalized para-K?hler spaces in Eisenhart?s sense. Also, we examine some invariant geometric objects with respect to equitorsion holomorphically projective mappings. These geometric objects reduce to the para-holomorphic projective curvature tensor in case of holomorphically projective mappings between usual para-K?hler spaces.

scholarly journals Deszcz Pseudo Symmetry Type LP-Sasakian Manifolds

2016 ◽  
Vol 54 (1) ◽  
pp. 35-53
Author(s):  
Kanak Kanti Baishya ◽  
Partha Roy Chowdhury
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Symmetry Type ◽  
Sasakian Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Concircular Curvature Tensor ◽  
Curvature Tensors

Abstract Recently the present authors introduced the notion of generalized quasi-conformal curvature tensor which bridges Conformal curvature tensor, Concircular curvature tensor, Projective curvature tensor and Conharmonic curvature tensor. This paper attempts to charectrize LP-Sasakian manifolds with ω(X, Y) · 𝒲 = L{(X ∧ɡ Y) · 𝒲}. On the basis of this curvature conditions and by taking into account, the permutation of different curvature tensors we obtained and tabled the nature of the Ricci tensor for the respective pseudo symmetry type LP-Sasakian manifolds.

scholarly journals On Almost C(a)-Manifold Satisfying Some Conditions On The Weyl Projective Curvature Tensor

2018 ◽  
Vol 15 ◽  
pp. 8145-8154
Author(s):  
Umit Yildirim
Keyword(s):  
Curvature Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Curvature Tensors

In the present paper, we have studied the curvature tensors of almost C()-manifolds satisfying the conditions P(,X)R = 0, P(,X) e Z = 0, P(,X)P = 0, P(,X)S = 0 and P(,X) e  C = 0. According these cases, we classified almost C()-manifolds.

A spacetime with pseudo-projective curvature tensor

2016 ◽  
Vol 57 (6) ◽  
pp. 062501 ◽  
Author(s):  
Sahanous Mallick ◽  
Young Jin Suh ◽  
Uday Chand De
Keyword(s):  
Curvature Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor

scholarly journals On projective-symmetric spaces

1964 ◽  
Vol 4 (1) ◽  
pp. 113-121 ◽  
Author(s):  
Bandana Gupta
Keyword(s):  
Symmetric Space ◽  
Curvature Tensor ◽  
Symmetric Spaces ◽  
Covariant Differentiation ◽  
Metric Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Image Position ◽  
Riemannian Spaces

This paper deals with a type of Remannian space Vn (n ≧ 2) for which the first covariant dervative of Weyl's projective curvature tensor is everywhere zero, that is where comma denotes covariant differentiation with respect to the metric tensor gij of Vn. Such a space has been called a projective-symmetric space by Gy. Soós [1]. We shall denote such an n-space by ψn. It will be proved in this paper that decomposable Projective-Symmetric spaces are symmetric in the sense of Cartan. In sections 3, 4 and 5 non-decomposable spaces of this kind will be considered in relation to other well-known classes of Riemannian spaces defined by curvature restrictions. In the last section the question of the existence of fields of concurrent directions in a ψ will be discussed.

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