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 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 Generalized Sasakian-Space-Forms with Projective Curvature Tensor

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
A. Sarkar ◽  
Ali Akbar
Keyword(s):  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Space Forms ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Sasakian Space Forms ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Metric Connection ◽  
Projective Curvature Tensor

AbstractThe object of the present paper is to study Ф-projectively flat generalized Sasakian-space-forms, projectively locally symmetric generalized Sasakian-space-forms and projectively locally Ф-symmetric generalized Sasakian-space-forms. All the obtained results are in the form of necessary and sufficient conditions. Interesting relations between projective curvature tensor and conformal curvature tensor of a generalized Sasakian-spaceform of dimension greater than three have been established. Some of these properties are also analyzed in the light of quarter-symmetric metric connection, in addition with the Levi-Civita connection. Obtained results are supported by illustrative examples.

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 On the Weyl projective curvature tensor of the projective semi-symmetric connection in an SP-Sasakian manifold

2020 ◽  
Vol 32 (9) ◽  
pp. 100-110
Author(s):  
TEERATHRAM RAGHUWANSHI ◽  
◽  
SHRAVAN KUMAR PANDEY ◽  
MANOJ KUMAR PANDEY ◽  
ANIL GOYAL ◽  
...  
Keyword(s):  
Curvature Tensor ◽  
Einstein Manifold ◽  
Sasakian Manifold ◽  
Projective Curvature ◽  
Symmetric Connection ◽  
Projective Curvature Tensor

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.

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 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.

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 ∗-Conformal η-Ricci soliton on Sasakian manifold

2021 ◽  
pp. 2250035
Author(s):  
Soumendu Roy ◽  
Santu Dey ◽  
Arindam Bhattacharyya ◽  
Shyamal Kumar Hui
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Ricci Soliton ◽  
Sasakian Manifolds ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor

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.

scholarly journals ON THE $\mathcal{M}$--PROJECTIVE CURVATURE TENSOR OF A $(k, \mu)$-CONTACT METRIC MANIFOLD

2017 ◽  
pp. 117
Author(s):  
D. G. Prakasha ◽  
Kakasab Mirji
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Sasakian Manifold ◽  
Riemannian Curvature ◽  
Contact Metric Manifold ◽  
Contact Metric Manifolds ◽  
Riemannian Curvature Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor

The paper deals with the study of $\mathcal{M}$-projective curvature tensor on $(k, \mu)$-contact metric manifolds. We classify non-Sasakian $(k, \mu)$-contact metric manifold satisfying the conditions $R(\xi, X)\cdot \mathcal{M} = 0$ and $\mathcal{M}(\xi, X)\cdot S =0$, where $R$ and $S$ are the Riemannian curvature tensor and the Ricci tensor, respectively. Finally, we prove that a $(k, \mu)$-contact metric manifold with vanishing extended $\mathcal{M}$-projective curvature tensor $\mathcal{M}^{e}$ is a Sasakian manifold.

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

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