scholarly journals QUASI-CONFORMAL CURVATURE TENSOR ON SASAKIAN MANIFOLDS

2017 ◽  
Vol 22 (1) ◽  
pp. 94-98
Author(s):  
Riddhi Jung Shah ◽  
N. V. C. Shukla
Keyword(s):  
Curvature Tensor ◽  
Einstein Manifold ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Conformally Recurrent

In this paper we studied some curvature properties of quasi-conformal curvature tensor on Sasakian manifolds. We have proven that a -dimensional Sasakian manifold satisfying the curvature conditions and is an Einstein manifold. We have also obtained some results on quasi-conformally recurrent Sasakian manifold. Finally, Sasakian manifold satisfying the condition was studied. 12n 0 ., S Y XR0 ., W Y XR0 divWJournal of Institute of Science and TechnologyVolume 22, Issue 1, July 2017, Page: 94-98

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 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.

scholarly journals On contact conformal curvature tensor in trans-Sasakian manifolds

BIBECHANA ◽  
2014 ◽  
Vol 12 ◽  
pp. 80-88
Author(s):  
Riddhi Jung Shah
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Conformally Flat ◽  
Sasakian Manifolds ◽  
3 Dimensional ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
In Trans

The purpose of this paper is to study some results on contact conformal curvature tensor in trans-Sasakian manifolds. Contact conformally flat trans-Sasakian manifold, ζ-contact conformally flat trans-Sasakian manifold and curvature conditions C0(ζ.X).S = 0 and C0(ζ.X).C0 = 0 are studied with some interesting results. Finally, we study an example of 3-dimensional trans-Sasakian manifold. DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11783  BIBECHANA 12 (2015) 80-88

scholarly journals Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Bilal Eftal Acet ◽  
Erol Kılıç ◽  
Selcen Yüksel Perktaş
Keyword(s):  
Curvature Tensor ◽  
Einstein Manifold ◽  
Constant Scalar Curvature ◽  
Sasakian Manifold ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Concircular Curvature Tensor

We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is anη-Einstein manifold. We also investigate some properties of curvature tensor, conformal curvature tensor,W2-curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor with respect to canonical paracontact connection on a para-Sasakian manifold. It is shown that a concircularly flat para-Sasakian manifold with respect to canonical paracontact connection is of constant scalar curvature. We give some characterizations for pseudo-projectively flat para-Sasakian manifolds.

scholarly journals On conformally recurrent spaces of second order

1969 ◽  
Vol 10 (1-2) ◽  
pp. 155-161 ◽  
Author(s):  
M. C. Chaki ◽  
A. N. Roy Chowdhury
Keyword(s):  
Curvature Tensor ◽  
Second Order ◽  
Covariant Differentiation ◽  
Metric Tensor ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Image Position ◽  
Conformally Recurrent ◽  
Zero Vector ◽  
Riemannian Spaces

In a recent paper [1] Adati and Miyazawa studied conformally recurrent spaces, that is, Riemannian spaces defined by where is the conformal curvature tensor: λi is a non-zero vector and comma denotes covariant differentiation with respect to the metric tensor gij.

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

scholarly journals On contact conformal curvature tensor in LP-Sasakian manifolds

BIBECHANA ◽  
2017 ◽  
Vol 15 ◽  
pp. 24-29
Author(s):  
Riddhi Jung Shah
Keyword(s):  
Curvature Tensor ◽  
Conformally Flat ◽  
Sasakian Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor

The purpose of the present paper is to study the contact conformal curvature tensor in LP-Sasakian manifolds. Some properties of contact conformally flat, ξ -contact conformally flat and contact conformally semi-symmetric LP-Sasakian manifolds are obtained.BIBECHANA 15 (2018) 24-29

scholarly journals On some classes of generalized quasi Einstein manifolds

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 443-456 ◽  
Author(s):  
Sinem Güler ◽  
Sezgin Demirbağ
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Einstein Manifold ◽  
Sufficient Conditions ◽  
Riemannian Curvature ◽  
Einstein Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Riemannian Curvature Tensor ◽  
Concircular Curvature Tensor

In the present paper, we investigate generalized quasi Einstein manifolds satisfying some special curvature conditions R?S = 0,R?S = LSQ(g,S), C?S = 0,?C?S = 0,?W?S = 0 and W2?S = 0 where R, S, C,?C,?W and W2 respectively denote the Riemannian curvature tensor, Ricci tensor, conformal curvature tensor, concircular curvature tensor, quasi conformal curvature tensor and W2-curvature tensor. Later, we find some sufficient conditions for a generalized quasi Einstein manifold to be a quasi Einstein manifold and we show the existence of a nearly quasi Einstein manifolds, by constructing a non trivial example.

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