projective curvature
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Author(s):  
Manisha Maheshkumar Kankarej

In the present paper, I studied different types of Curvature like Riemannian Curvature, Concircular Curvature, Weyl Curvature, and Projective Curvature in Quarter Symmetric non-Metric Connection in P-Sasakian manifold. A comparative study of a manifold with a Riemannian connection is done with a P-Sasakian Manifold. Conditions for vanishing for different types of curvature are also a part of the study. Some necessary properties of the Hessian operator are discussed with respect to all curvatures as well.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Shanmukha ◽  
V. Venkatesha

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.


Author(s):  
Soumendu Roy ◽  
Santu Dey ◽  
Arindam Bhattacharyya ◽  
Shyamal Kumar Hui

In this paper, we study ∗-Conformal [Formula: see text]-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting ∗-Conformal [Formula: see text]-Ricci soliton. We obtain some significant results on ∗-Conformal [Formula: see text]-Ricci soliton in Sasakian manifolds satisfying [Formula: see text], [Formula: see text], [Formula: see text] [Formula: see text], where [Formula: see text] is Pseudo-projective curvature tensor. The conditions for ∗-Conformal [Formula: see text]-Ricci soliton on [Formula: see text]-conharmonically flat and [Formula: see text]-projectively flat Sasakian manifolds have been obtained in this paper. Lastly we give an example of five-dimensional Sasakian manifolds satisfying ∗-Conformal [Formula: see text]-Ricci soliton.


2021 ◽  
Vol 45 (02) ◽  
pp. 237-258
Author(s):  
ABSOS ALI SHAIKH ◽  
TRAN QUOC BINH ◽  
HARADHAN KUNDU

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.


2020 ◽  
Vol 32 (9) ◽  
pp. 100-110
Author(s):  
TEERATHRAM RAGHUWANSHI ◽  
◽  
SHRAVAN KUMAR PANDEY ◽  
MANOJ KUMAR PANDEY ◽  
ANIL GOYAL ◽  
...  

The objective of the present paper is to study the W2-curvature tensor of the projective semi-symmetric connection in an SP-Sasakian manifold. It is shown that an SP-Sasakian manifold satisfying the conditions ܲ\simP ⋅W2\sim ܹ = 0 is an Einstein manifold and ܹW2\sim . ܲP\sim = 0 is a quasi Einstein manifold.


2020 ◽  
Vol 26 (3) ◽  
pp. 369-379
Author(s):  
Abhijit Mandal ◽  
Ashoke Das

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.


Author(s):  
S. K. Tiwari ◽  
Ved Mani

The present communication has been devoted to the study of projective motion, projective curvature collineation and infinitesimal projective transformation in a Finsler space equipped with semi-symmetric connection. In this communication we have derived results in the form of theorems which hold when the Finsler space under consideration admits both projective motion and projective curvature collineation and in this continuation, we have also derived the relationships which hold when the space under consideration admits a non-affine as well as an affine infinitesimal projective transformation.


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