scholarly journals On Generalized ϕ-Recurrent (ϵ,δ)-Trans-Sasakian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
C. S. Bagewadi ◽  
Dakshayani A. Patil
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Characteristic Vector ◽  
Sasakian Manifolds ◽  
Characteristic Vector Field

We study generalized ϕ-recurrent (ϵ,δ)-trans-Sasakian manifolds. A relation between the associated 1-forms A and B and relation between characteristic vector field ξ and the vector fields ρ1, ρ2 for a generalized ϕ-recurrent.

scholarly journals On Lightlike Geometry of Para-Sasakian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Bilal Eftal Acet ◽  
Selcen Yüksel Perktaş ◽  
Erol Kılıç
Keyword(s):  
Vector Field ◽  
Characteristic Vector ◽  
Sasakian Manifolds ◽  
Lightlike Hypersurface ◽  
Sasakian Structure ◽  
Integrability Conditions ◽  
Integrable Distribution ◽  
Lightlike Hypersurfaces ◽  
Characteristic Vector Field

We study lightlike hypersurfaces of para-Sasakian manifolds tangent to the characteristic vector field. In particular, we define invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, respectively, and give examples. Integrability conditions for the distributions on a screen semi-invariant lightlike hypersurface of para-Sasakian manifolds are investigated. We obtain a para-Sasakian structure on the leaves of an integrable distribution of a screen semi-invariant lightlike hypersurface.

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 Existence of some classes of N(k)-quasi Einstein manifolds

2021 ◽  
Vol 39 (5) ◽  
pp. 145-162
Author(s):  
Sudhakar Kumar Chaubey ◽  
K. K. Bhaishya ◽  
M. Danish Siddiqi
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Unit Vector ◽  
Characteristic Vector ◽  
Einstein Manifolds ◽  
Unit Vector Fields ◽  
Characteristic Vector Field

The object of the present paper is to study some classes of N(k)-quasi Einstein manifolds. The existence of such manifolds are proved by giving non-trivial physical and geometrical examples. It is also proved that the characteristic vector field of the manifold is killing as well as parallel unit vector fields under certain curvaturerestrictions.

scholarly journals Harmonic characteristic vector fields on contact metric three-manifolds

2003 ◽  
Vol 67 (2) ◽  
pp. 305-315 ◽  
Author(s):  
Domenico Perrone
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Harmonic Map ◽  
Characteristic Vector ◽  
Dense Open Subset ◽  
Sphere Bundle ◽  
Sasaki Metric ◽  
Characteristic Vector Field ◽  
Characteristic Vector Fields ◽  
Unit Tangent Sphere Bundle

In this paper we show that a contact metric three-manifold is a generalised (k, μ)-space on an everywhere dense open subset if and only if its characteristic vector field ξ determines a harmonic map from the manifold into its unit tangent sphere bundle equipped with the Sasaki metric. Moreover, we classify the contact metric three-manifolds whose characteristic vector field ξ is strongly normal (or equivalently, is harmonic and minimal).

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 Ricci semisymmetric almost Kenmotsu manifolds with nullity distributions

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 179-186
Author(s):  
Sharief Deshmukh ◽  
Uday De ◽  
Peibiao Zhao
Keyword(s):  
Vector Field ◽  
Characteristic Vector ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Nullity Distribution ◽  
Characteristic Vector Field

The object of the present paper is to characterize Ricci semisymmetric almost Kenmotsu manifolds with its characteristic vector field ? belonging to the (k,?)'-nullity distribution and (k,?)-nullity distribution respectively. Finally, an illustrative example is given.

scholarly journals Certain results on N(k)-contact metric manifolds

2018 ◽  
Vol 49 (3) ◽  
pp. 205-220
Author(s):  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Three Dimensional ◽  
Characteristic Vector ◽  
Ricci Solitons ◽  
Gradient Ricci Solitons ◽  
Contact Metric Manifolds ◽  
Nullity Distribution ◽  
Characteristic Vector Field

In the present paper we study contact metric manifolds whose characteristic vector field $\xi$ belonging to the $k$-nullity distribution. First we consider concircularly pseudosymmetric $N(k)$-contact metric manifolds of dimension $(2n+1)$. Beside these, we consider Ricci solitons and gradient Ricci solitons on three dimensional $N(k)$-contact metric manifolds. As a consequence we obtain several results. Finally, an example is given.

Sign in / Sign up

Export Citation Format

Share Document