scholarly journals On the topology of Sasakian manifolds

2003 ◽  
Vol 93 (1) ◽  
pp. 99 ◽  
Author(s):  
Gheorghe Pitiş
Keyword(s):  
Vector Field ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Bisectional Curvature

The notion of $q$-bisectional curvature of a Sasakian manifold $M$ is defined. It is proved that if $M$ has lower bounded $q$-bisectional curvature and contains a compact invariant submanifold tangent to the structure vector field then $M$ is compact. Myers and Frankel type theorems for Sasakian manifolds with lower bounded and positive $q$-bisectional curvature, respectively, are also given.

Some Properties of Para-Sasakian Manifolds

2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Sasakian Manifold ◽  
Subject Classification ◽  
Killing Vector Field ◽  
Sasakian Manifolds ◽  
Geometric Properties ◽  
Paper Author

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.

Anti-invariant Riemannian submersions from Sasakian manifolds with totally umbilical fibers

2021 ◽  
pp. 2150169
Author(s):  
Gizem Köprülü ◽  
Bayram Şahin
Keyword(s):  
Vector Field ◽  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Sasakian Manifold ◽  
Riemannian Submersion ◽  
Sasakian Manifolds ◽  
Riemannian Submersions ◽  
Totally Umbilical ◽  
Characteristic Vector Field ◽  
Horizontal Vector

The purpose of this paper is to study anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds such that characteristic vector field is vertical or horizontal vector field. We first show that any anti-invariant Riemannian submersions from Sasakian manifold is not a Riemannian submersion with totally umbilical fiber. Then we introduce anti-invariant Riemannian submersions from Sasakian manifolds with totally contact umbilical fibers. We investigate the totally contact geodesicity of fibers of such submersions. Moreover, under this condition, we investigate Ricci curvature of anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds.

scholarly journals On trans-Sasakian $3$-manifolds as $\eta$-Einstein solitons

2021 ◽  
Vol 13 (2) ◽  
pp. 460-474
Author(s):  
D. Ganguly ◽  
S. Dey ◽  
A. Bhattacharyya
Keyword(s):  
Vector Field ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
3 Dimensional ◽  
Codazzi Type

The present paper is to deliberate the class of $3$-dimensional trans-Sasakian manifolds which admits $\eta$-Einstein solitons. We have studied $\eta$-Einstein solitons on $3$-dimensional trans-Sasakian manifolds where the Ricci tensors are Codazzi type and cyclic parallel. We have also discussed some curvature conditions admitting $\eta$-Einstein solitons on $3$-dimensional trans-Sasakian manifolds and the vector field is torse-forming. We have also shown an example of $3$-dimensional trans-Sasakian manifold with respect to $\eta$-Einstein soliton to verify our results.

scholarly journals Ricci Solitons in α-Sasakian Manifolds

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Gurupadavva Ingalahalli ◽  
C. S. Bagewadi
Keyword(s):  
Vector Field ◽  
Sasakian Manifold ◽  
Ricci Soliton ◽  
Second Order ◽  
Ricci Solitons ◽  
Sasakian Manifolds ◽  
Constant Multiple ◽  
Metric Tensor ◽  
3 Dimensional

We study Ricci solitons in α-Sasakian manifolds. It is shown that a symmetric parallel second order-covariant tensor in a α-Sasakian manifold is a constant multiple of the metric tensor. Using this, it is shown that if ℒVg+2S is parallel where V is a given vector field, then (g,V,λ) is Ricci soliton. Further, by virtue of this result, Ricci solitons for n-dimensional α-Sasakian manifolds are obtained. Next, Ricci solitons for 3-dimensional α-Sasakian manifolds are discussed with an example.

scholarly journals On the Sharp Dimension Estimate of CR Holomorphic Functions in Sasakian Manifolds

2019 ◽  
Author(s):  
Shu-Cheng Chang ◽  
Yingbo Han ◽  
Chien Lin
Keyword(s):  
Sasakian Manifold ◽  
Holomorphic Functions ◽  
Sasakian Manifolds ◽  
Kahler Geometry ◽  
Bisectional Curvature ◽  
Dimension Estimate ◽  
Pseudohermitian Manifold

Abstract This is the very 1st paper to focus on the CR analogue of Yau’s uniformization conjecture in a complete noncompact pseudohermitian $(2n+1)$-manifold of vanishing torsion (i.e., Sasakian manifold), which is an odd dimensional counterpart of Kähler geometry. In this paper, we mainly deal with the problem of the sharp dimension estimate of CR holomorphic functions in a complete noncompact pseudohermitian manifold of vanishing torsion with nonnegative pseudohermitian bisectional curvature.

On η-Einstein Trans-Sasakian Manifolds

2011 ◽  
Vol 57 (2) ◽  
pp. 417-440
Author(s):  
Falleh Al-Solamy ◽  
Jeong-Sik Kim ◽  
Mukut Tripathi
Keyword(s):  
Vector Field ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Manifolds ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
3 Dimensional ◽  
Almost Contact Metric ◽  
Necessary And Sufficient

On η-Einstein Trans-Sasakian ManifoldsA systematic study of η-Einstein trans-Sasakian manifold is performed. We find eight necessary and sufficient conditions for the structure vector field ζ of a trans-Sasakian manifold to be an eigenvector field of the Ricci operator. We show that for a 3-dimensional almost contact metric manifold (M,φ, ζ, η, g), the conditions of being normal, trans-K-contact, trans-Sasakian are all equivalent to ∇ζ ∘ φ = φ ∘ ∇ζ. In particular, the conditions of being quasi-Sasakian, normal with 0 = 2β = divζ, trans-K-contact of type (α, 0), trans-Sasakian of type (α, 0), andC6-class are all equivalent to ∇ ζ = -αφ, where 2α = Trace(φ∇ζ). In last, we give fifteen necessary and sufficient conditions for a 3-dimensional trans-Sasakian manifold to be η-Einstein.

Biharmonic Hypersurfaces of LP-Sasakian Manifolds

2011 ◽  
Vol 57 (2) ◽  
pp. 387-408 ◽  
Author(s):  
Selcen Perktaş ◽  
Erol Kiliç ◽  
Sadik Keleş
Keyword(s):  
Vector Field ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Characteristic Vector ◽  
Normal Vector ◽  
Sasakian Manifolds ◽  
Normal Vector Field ◽  
Characteristic Vector Field

Biharmonic Hypersurfaces of LP-Sasakian Manifolds In this paper the biharmonic hypersurfaces of Lorentzian para-Sasakian manifolds are studied. We firstly find the biharmonic equation for a hypersurface which admits the characteristic vector field of the Lorentzian para-Sasakian as the normal vector field. We show that a biharmonic spacelike hypersurface of a Lorentzian para-Sasakian manifold with constant mean curvature is minimal. The biharmonicity condition for a hypersurface of a Lorentzian para-Sasakian manifold is investigated when the characteristic vector field belongs to the tangent hyperplane of the hypersurface. We find some necessary and sufficient conditions for a timelike hypersurface of a Lorentzian para-Sasakian manifold to be proper biharmonic. The nonexistence of proper biharmonic timelike hypersurfaces with constant mean curvature in a Ricci flat Lorentzian para-Sasakian manifold is proved.

scholarly journals Submanifolds of Sasakian Manifolds with Certain Parallel Operators

ISRN Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Amira A. Ishan
Keyword(s):  
Tensor Field ◽  
Sasakian Manifold ◽  
Symmetric Tensor ◽  
Sasakian Manifolds ◽  
Invariant Submanifold

We study submanifolds of Sasakian manifolds and obtain a condition under which certain naturally defined symmetric tensor field on the submanifold is to be parallel and use this result to obtain conditions under which a submanifold of the Sasakian manifold is an invariant submanifold.

scholarly journals Skew semi-invariant submanifolds of generalized quasi-Sasakian manifolds

2018 ◽  
Vol 9 (2) ◽  
pp. 188-197 ◽  
Author(s):  
M.D. Siddiqi ◽  
A. Haseeb ◽  
M. Ahmad
Keyword(s):  
Sasakian Manifold ◽  
Equivalence Relations ◽  
Cr Manifold ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
New Class ◽  
Almost Contact Metric ◽  
Invariant Submanifolds

In the present paper,  we study a new class of submanifolds of a generalized Quasi-Sasakian manifold, called skew semi-invariant submanifold. We obtain integrability conditions of the distributions on a skew semi-invariant submanifold and also find the condition for a skew semi-invariant submanifold  of a generalized Quasi-Sasakian manifold to be mixed totally geodesic. Also it is shown that a  skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold will be anti-invariant if and only if $A_{\xi}=0$; and the submanifold will be skew semi-invariant submanifold if $\nabla w=0$. The equivalence relations for the  skew semi-invariant submanifold of a  generalized Quasi-Sasakian manifold are given. Furthermore, we have proved that a skew semi-invariant $\xi^\perp$-submanifold of a normal almost contact metric manifold and a generalized Quasi-Sasakian manifold with non-trivial invariant distribution is $CR$-manifold. An example of dimension 5 is given to show that a skew semi-invariant $\xi^\perp$ submanifold is a $CR$-structure on the manifold.

scholarly journals On Totally Contact Umbilical Contact CR-Lightlike Submanifolds Of Indefinite Sasakian Manifolds

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Manish Gogna ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sasakian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

AbstractAfter brief introduction, we prove that a totally contact umbilical CR- lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold. Finally, we characterize a contact CR-lightlike submanifold of indefinite Sasakian manifold to be a contact CR-lightlike product

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