ON PARA-SASAKIAN MANIFOLDS ADMITTING GENERALIZED B CURVATURE TENSOR

2019 ◽  
Vol 119 (2) ◽  
pp. 141-151
Author(s):  
Venkatesha ◽  
B. Phalaksha Murthy ◽  
R. T. Naveen Kumar
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifolds

scholarly journals m - projective curvature tensor on a Lorentzian para – Sasakian manifolds

2013 ◽  
Vol 6 (1) ◽  
pp. 19-23 ◽  
Author(s):  
Amit Prakash Amit Prakash
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifolds ◽  
Projective Curvature ◽  
Projective Curvature Tensor

scholarly journals Some characterizations of three-dimensional trans-Sasakian manifolds admitting η- Ricci solitons and trans-Sasakian manifolds as Kagan subprojective space

2020 ◽  
Vol 72 (3) ◽  
pp. 427-432
Author(s):  
A. Sarkar ◽  
A. Sil ◽  
A. K. Paul
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Three Dimensional ◽  
Ricci Soliton ◽  
Second Order ◽  
Ricci Solitons ◽  
Riemann Curvature ◽  
Sasakian Manifolds ◽  
Riemann Curvature Tensor ◽  
Order Parallel

UDC 514.7 The object of the present paper is to study three-dimensional trans-Sasakian manifolds admitting η -Ricci soliton. Actually, we study such manifolds whose Ricci tensor satisfy some special conditions like cyclic parallelity, Ricci semisymmetry, ϕ -Ricci semisymmetry, after reviewing the properties of second order parallel tensors on such manifolds. We determine the form of Riemann curvature tensor of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces. We also give some classification results of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces.

scholarly journals SASAKIAN MANIFOLDS WITH QUASI-CONFORMAL CURVATURE TENSOR

2008 ◽  
Vol 45 (2) ◽  
pp. 313-319 ◽  
Author(s):  
Uday Chand De ◽  
Jae-Bok Jun ◽  
Abul Kalam Gazi
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor

scholarly journals Sasakian manifolds with vanishing contact Bochner curvature tensor and constant scalar curvature

1977 ◽  
Vol 37 (1) ◽  
pp. 113-122 ◽  
Author(s):  
Toshihiko Ikawa ◽  
Masahiro Kon
Keyword(s):  
Scalar Curvature ◽  
Curvature Tensor ◽  
Constant Scalar Curvature ◽  
Sasakian Manifolds

scholarly journals On D-conformal Curvature Tensor Sasakian Manifolds

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
A. Taleshian ◽  
A. A. Hosseinzadeh ◽  
F. Khaniani
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor

On M-Projective Curvature Tensor of Lorentzian α-Sasakian Manifolds

2017 ◽  
Vol 18 ◽  
pp. 22-31
Author(s):  
D.G. Prakasha ◽  
Vasant Chavan
Keyword(s):  
Curvature Tensor ◽  
Unit Sphere ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor

In this paper, we study the nature of Lorentzianα-Sasakian manifolds admitting M-projective curvature tensor. We show that M-projectively flat and irrotational M-projective curvature tensor of Lorentzian α-Sasakian manifolds are locally isometric to unit sphere Sn(c) , wherec = α2. Next we study Lorentzianα-Sasakian manifold with conservative M-projective curvature tensor. Finally, we find certain geometrical results if the Lorentzianα-Sasakian manifold satisfying the relation M(X,Y)⋅R=0.

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 Some Curvature Properties of D-conformal Curvature Tensor on LP-Sasakian Manifolds

2015 ◽  
Vol 19 (1) ◽  
pp. 30-34
Author(s):  
Riddhi Jung Shah
Keyword(s):  
Curvature Tensor ◽  
Science And Technology ◽  
Sasakian Manifold ◽  
Conformally Flat ◽  
Sasakian Manifolds ◽  
Curvature Condition ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor

This paper deals with the study of geometry of Lorentzian para-Sasakian manifolds. We investigate some properties of D-conformally flat, D-conformally semi-symmetric, Xi-D-conformally flat and Phi-D-conformally flat curvature conditions on Lorentzian para-Sasakian manifolds. Also it is proved that in each curvature condition an LP-Sasakian manifold (Mn,g)(n>3) is an eta-Einstein manifold.Journal of Institute of Science and Technology, 2014, 19(1): 30-34

scholarly journals Quarter-symmetric metric connection in a P-Sasakian manifold

2015 ◽  
Vol 53 (1) ◽  
pp. 137-150 ◽  
Author(s):  
Krishanu Mandal ◽  
Uday Chand De
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Metric Connection

Abstract In this paper, we consider a quarter-symmetric metric connection in a P-Sasakian manifold. We investigate the curvature tensor and the Ricci tensor of a P-Sasakian manifold with respect to the quarter-symmetric metric connection. We consider semisymmetric P-Sasakian manifold with respect to the quarter- symmetric metric connection. Furthermore, we consider generalized recurrent P-Sasakian manifolds and prove the non-existence of recurrent and pseudosymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Finally, we construct an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection which verifies Theorem 4.1.

scholarly journals Quarter-Symmetric Nonmetric Connection on P-Sasakian Manifolds

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Abul Kalam Mondal ◽  
U. C. De
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Second Order ◽  
Sasakian Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Metric Connection ◽  
Concircular Curvature Tensor ◽  
Order Parallel

The object of the present paper is to study a quarter-symmetric nonmetric connection on a P-Sasakian manifold. In this paper we consider the concircular curvature tensor and conformal curvature tensor on a P-Sasakian manifold with respect to the quarter-symmetric nonmetric connection. Next we consider second-order parallel tensor with respect to the quarter-symmetric non-metric connection. Finally we consider submanifolds of an almost paracontact manifold with respect to a quarter-symmetric non-metric connection.

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