scholarly journals Some properties of ET-projective tensors obtained from Weyl projective tensor

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 573-584
Author(s):  
Mica Stankovic ◽  
Milan Zlatanovic ◽  
Nenad Vesic
Keyword(s):  
Curvature Tensor ◽  
Affine Connection ◽  
Connection Coefficients ◽  
Linearly Independent ◽  
Projective Curvature ◽  
Projective Tensor ◽  
Connection Space ◽  
Curvature Tensors

Vanishing of linearly independent curvature tensors of a non-symmetric affine connection space as functions of vanished curvature tensor of the associated space of this one are analyzed in the first part of this paper. Projective curvature tensors of a non-symmetric affine connection space are expressed as functions of the affine connection coefficients and Weyl projective tensor of the corresponding associated affine connection space in the second part of this paper.

scholarly journals On semisymmetric connection

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1179-1184
Author(s):  
Ana Velimirovic ◽  
Milan Zlatanovic
Keyword(s):  
Symmetric Space ◽  
Curvature Tensor ◽  
The Other ◽  
Linear Combinations ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Curvature Tensors

Using the non-symmetry of a connection, it is possible to introduce four types of covariant derivatives. Based on these derivatives, several types of Ricci?s identities and twelve curvature tensors are obtained. Five of them are linearly independent but the other curvature tensors can be expressed as linear combinations of these five linearly independent curvature tensors and the curvature tensor of the corresponding associated symmetric space. The semisymmetric connection is defined and the properties of two of the five independent curvature tensors are analyzed. In the same manner, the properties for three others curvature tensors may be derived.

About differential equations of the curvature tensors of a fundamental group and affine connections

2019 ◽  
pp. 133-140
Author(s):  
N. Ryazanov
Keyword(s):  
Differential Equations ◽  
Fundamental Group ◽  
Curvature Tensor ◽  
Principal Bundle ◽  
Group Structure ◽  
Affine Connection ◽  
Affine Connections ◽  
First Order ◽  
Structure Equations ◽  
Curvature Tensors

The principal bundle is considered, the base of which is an n-dimensional smooth manifold, and the typical fiber is an r-fold Lie group. Structure equations for the forms of the fundamental group and affine connections are given, each of which contains the corresponding components of the curvature tensor. For each connection, an approach is shown that allows to find the differential equations for the components of the curvature tensor of the corresponding connection in a faster way than by differentiating the expressions of these objects in terms of the connection objects and their Pfaffian derivatives. The method consists in successively solving cubic equations, first by Laptev’s lemma, then by Cartan’s lemma. Taking into account the comparisons modulo basic forms, we obtain already known results (see [3]). Thus, differential equations are derived for the components of the curvature tensor of the first-order fundamentalgroup connection, as well as for the components of the curvature tensor of the affine connection.

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 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.

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 Some Results on Projective Curvature Tensor of Nearly Cosymplectic Manifold

2018 ◽  
Vol 11 (3) ◽  
pp. 823-833 ◽  
Author(s):  
Nawaf Jaber Mohammed ◽  
Habeeb Mtashar Abood
Keyword(s):  
Curvature Tensor ◽  
Einstein Space ◽  
Geometric Meaning ◽  
Cosymplectic Manifold ◽  
Projective Curvature ◽  
Projective Tensor ◽  
Nearly Cosymplectic ◽  
Projective Curvature Tensor

In the nearly cosymplectic manifold, dened a tensor of type (4,0), it's called a projective curvature tensor. In this article we discuss an interesting question; what the geometric meaning of this tensor when it's act on nearly cosymplectic manifold? The answer of this question leads to get an application on Einstein space. In particular, the necessary and sucient conditions that a projective tensor is vanishes are found.

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.

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