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 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 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 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 On the quasi-conformal curvature tensor of an almost Kenmotsu manifold with nullity distributions

2018 ◽  
Vol 33 (2) ◽  
pp. 255
Author(s):  
Dibakar Dey ◽  
Pradip Majhi
Keyword(s):  
Vector Field ◽  
Curvature Tensor ◽  
Conformally Flat ◽  
Kenmotsu Manifold ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Nullity Distribution ◽  
Characteristic Vector Field

The object of the present paper is to characterize quasi-conformally flat and $\xi$-quasi-conformally flat almost Kenmotsu manifolds with  $(k,\mu)$-nullity and $(k,\mu)'$-nullity distributions respectively. Also we characterize almost Kenmotsu manifolds with vanishing extended quasi-conformal curvature tensor and extended $\xi$-quasi-conformally flat almost Kenmotsu manifolds such that the characteristic vector field $\xi$ belongs to the $(k,\mu)$-nullity distribution.

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 3-Dimensional Pseudo-Quasi-Conformal Curvature Tensor on (LCS)n-Manifolds

OALib ◽  
2019 ◽  
Vol 06 (06) ◽  
pp. 1-7
Author(s):  
Basavaraju Phalaksha Murthy ◽  
Venkatesha Venkatesha
Keyword(s):  
Curvature Tensor ◽  
3 Dimensional ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor

scholarly journals A new curvaturelike tensor field in an almost contact Riemannian manifold II

2018 ◽  
Vol 103 (117) ◽  
pp. 113-128 ◽  
Author(s):  
Koji Matsumoto
Keyword(s):  
Riemannian Manifold ◽  
Curvature Tensor ◽  
Tensor Field ◽  
Sasakian Manifold ◽  
Tensor Fields ◽  
Geometrical Properties ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Riemannian Curvature Tensor ◽  
Contact Riemannian Manifold

In the last paper, we introduced a new curvaturlike tensor field in an almost contact Riemannian manifold and we showed some geometrical properties of this tensor field in a Kenmotsu and a Sasakian manifold. In this paper, we define another new curvaturelike tensor field, named (CHR)3-curvature tensor in an almost contact Riemannian manifold which is called a contact holomorphic Riemannian curvature tensor of the second type. Then, using this tensor, we mainly research (CHR)3-curvature tensor in a Sasakian manifold. Then we define the notion of the flatness of a (CHR)3-curvature tensor and we show that a Sasakian manifold with a flat (CHR)3-curvature tensor is flat. Next, we introduce the notion of (CHR)3-?-Einstein in an almost contact Riemannian manifold. In particular, we show that Sasakian (CHR)3- ?-Einstein manifold is ?-Einstain. Moreover, we define the notion of (CHR)3- space form and consider this in a Sasakian manifold. Finally, we consider a conformal transformation of an almost contact Riemannian manifold and we get new invariant tensor fields (not the conformal curvature tensor) under this transformation. Finally, we prove that a conformally (CHR)3-flat Sasakian manifold does not exist.

scholarly journals Generalized sasakian-space-forms with D-conformal curvature tensor

2013 ◽  
Vol 8 (2) ◽  
pp. 48-56
Author(s):  
Riddhi Jung Shah
Keyword(s):  
Curvature Tensor ◽  
Conformally Flat ◽  
Curvature Condition ◽  
Space Forms ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Sasakian Space Forms ◽  
Engineering And Technology ◽  
Condition B

In this paper we study generalized Sasakian-space-forms with D-conformal curvature tensor. In generalized Sasakian-space-forms, we investigate some results on D-conformally flat, ?-D-conformally flat, ?-D-conformally flat and the curvature condition B(? ?).S=0. Kathmandu University Journal of Science, Engineering and Technology Vol. 8, No. II, December, 2012, 48-56 DOI: http://dx.doi.org/10.3126/kuset.v8i2.7325

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