scholarly journals INTEGRAL CURVES OF THE CHARACTERISTIC VECTOR FIELD ON CR-SUBMANIFOLDS OF MAXIMAL CR-DIMENSION

2017 ◽  
Vol 32 (1) ◽  
pp. 107-118
Author(s):  
Hyang Sook Kim ◽  
Jin Suk Pak
Keyword(s):  
Vector Field ◽  
Characteristic Vector ◽  
Integral Curves ◽  
Characteristic Vector Field ◽  
Cr Submanifolds

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 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.

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.

scholarly journals On almost Kenmotsu manifolds with nullity distributions

2017 ◽  
Vol 48 (3) ◽  
pp. 251-262 ◽  
Author(s):  
Uday Chand De ◽  
Jae Bok Jun ◽  
Krishanu Mandal
Keyword(s):  
Vector Field ◽  
Curvature Tensor ◽  
Characteristic Vector ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Projective Curvature ◽  
Nullity Distribution ◽  
Projective Curvature Tensor ◽  
Characteristic Vector Field

The object of this paper is to characterize the curvature conditions $R\cdot P=0$ and $P\cdot S=0$ with its characteristic vector field $\xi$ belonging to the $(k,\mu)'$-nullity distribution and $(k,\mu)$-nullity distribution respectively, where $P$ is the Weyl projective curvature tensor. As a consequence of the main results we obtain several corollaries.

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 Critical associated metrics on contact manifolds III

1991 ◽  
Vol 50 (2) ◽  
pp. 189-196 ◽  
Author(s):  
David E. Blair
Keyword(s):  
Vector Field ◽  
Contact Structure ◽  
Contact Manifold ◽  
Characteristic Vector ◽  
Sphere Bundle ◽  
Contact Manifolds ◽  
Parameter Group ◽  
Group Of Isometries ◽  
Characteristic Vector Field ◽  
Regular Contact

AbstractIn the first paper of this series we studied on a compact regular contact manifold the integral of the Ricci curvature in the direction of the characteristic vector field considered as a functional on the set of all associated metrics. We showed that the critical points of this functional are the metrics for which the characteristic vector field generates a 1-parameter group of isometries and conjectured that the result might be true without the regularity of the contact structure. In the present paper we show that this conjecture is false by studying this problem on the tangent sphere bundle of a Riemannian manifold. In particular the standard associated metric is a critical point if and only if the base manifold is of constant curvature +1 or −1; in the latter case the characteristic vector field does not generate a 1-parameter group of isometries.

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