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 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 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 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 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 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 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 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 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.

Sign in / Sign up

Export Citation Format

Share Document