Projective Curvature Tensors of Some Special Manifolds with Non-symmetric Linear Connection

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Miloš Z. Petrović ◽  
Ana M. Velimirović
Keyword(s):  
Linear Connection ◽  
Projective Curvature ◽  
Curvature Tensors

scholarly journals Curvature Properties of Generalized pp-Wave Metrics

2021 ◽  
Vol 45 (02) ◽  
pp. 237-258
Author(s):  
ABSOS ALI SHAIKH ◽  
TRAN QUOC BINH ◽  
HARADHAN KUNDU
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Sufficient Condition ◽  
Type Condition ◽  
Pure Radiation ◽  
Projective Curvature ◽  
Pp Wave ◽  
Codazzi Type ◽  
Curvature Tensors ◽  
Special Case

The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metrics. It is shown that a generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spacetime is semisymmetric, semisymmetric due to conformal and projective curvature tensors, R-space by Venzi and satisfies the pseudosymmetric type condition P ⋅ P = −13Q(S,P). Again we investigate the sufficient condition for which a generalized pp-wave spacetime turns into pp-wave spacetime, pure radiation spacetime, locally symmetric and recurrent. Finally, it is shown that the energy-momentum tensor of pp-wave spacetime is parallel if and only if it is cyclic parallel. Again the energy momentum tensor is Codazzi type if it is cyclic parallel but the converse is not true as shown by an example. Finally, we make a comparison between the curvature properties of the Robinson-Trautman metric and generalized pp-wave metric.

PARALLEL π-VECTOR FIELDS AND ENERGY β-CHANGE

2011 ◽  
Vol 08 (04) ◽  
pp. 753-772 ◽  
Author(s):  
A. SOLEIMAN
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Finsler Geometry ◽  
Linear Connection ◽  
Free Form ◽  
Cartan Connection ◽  
Finsler Spaces ◽  
Chern Connection ◽  
Berwald Connection ◽  
Curvature Tensors

The present paper deals with an intrinsic investigation of the notion of a parallel π-vector field on the pullback bundle of a Finsler manifold (M, L). The effect of the existence of a parallel π-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular β-change, namely the energy β-change ([Formula: see text]with[Formula: see text] being a parallel π-vector field), is established. The relation between the two Barthel connections Γ and [Formula: see text], corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy β-change of the fundamental linear connection in Finsler geometry: The Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is concluded. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.

scholarly journals Relativistic segnificance of curvature tensors

1982 ◽  
Vol 5 (1) ◽  
pp. 133-139 ◽  
Author(s):  
G. P. Pokhariyal
Keyword(s):  
Electromagnetic Field ◽  
Vector Field ◽  
Electric Field ◽  
Gravitational Waves ◽  
Einstein Space ◽  
Geometrical Properties ◽  
Projective Curvature ◽  
Cyclic Property ◽  
Projective Curvature Tensor ◽  
Curvature Tensors

In thi paper new curvature tensors have been defined on the lines of Weyl's projective curvature tensor and it has been shown that the “distribution” (order in which the vectors in question are arranged before being acted upon by the tensor in question) of vector field over the metric potentials and matter tensors plays an important role in shaping the various physical and geometrical properties of a tensor viz the formulation of gravitational waves, reduction of electromagnetic field to a purely electric field, vanishing of the contracted tensor in an Einstein Space and the cyclic property.

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.

ENERGY β-CONFORMAL CHANGE IN FINSLER GEOMETRY

2012 ◽  
Vol 09 (04) ◽  
pp. 1250029 ◽  
Author(s):  
A. SOLEIMAN
Keyword(s):  
Vector Field ◽  
Finsler Geometry ◽  
Linear Connection ◽  
Finsler Manifold ◽  
Free Form ◽  
Cartan Connection ◽  
Chern Connection ◽  
Conformal Change ◽  
Berwald Connection ◽  
Curvature Tensors

The present paper deals with an intrinsic generalization of the conformal change and energy β-change on a Finsler manifold (M.L.), namely the energy β-conformal change ([Formula: see text] with [Formula: see text]; [Formula: see text] being a concurrent π-vector field and σ(x) is a function on M). The relation between the two Barthel connections Γ and [Formula: see text], corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy β-conformal change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is obtained. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.

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 RICCI AND PROJECTIVE CURVATURE TENSORS ON A TYPE OF PARA-KENMOTSU MANIFOLD

2016 ◽  
Vol 111 (2) ◽  
Author(s):  
S.S. Devi ◽  
K.L. Sai Prasad ◽  
G.V.S.R. Deekshitulu
Keyword(s):  
Kenmotsu Manifold ◽  
Projective Curvature ◽  
Curvature Tensors
Sign in / Sign up

Export Citation Format

Share Document