scholarly journals Some results on null hypersurfaces in $(LCS)$-manifolds

2019 ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Vector Field ◽  
Ricci Tensor ◽  
Characteristic Vector ◽  
Null Hypersurface ◽  
Conformally Flat ◽  
Totally Geodesic ◽  
Null Hypersurfaces ◽  
Characteristic Vector Field

We prove that a Lorentzian concircular structure $ (LCS)$-manifold does not admit any null hypersurface which is tangential or transversal to its characteristic vector field. Due to the above, we focus on its ascreen null hypersurfaces, and show that such hypersurfaces admit a symmetric Ricci tensor. Furthermore, we prove that there is no any totally geodesic ascreen null hypersurfaces of a conformally flat $(LCS)$-manifold.

scholarly journals INVARIANT SUBMANIFOLDS OF CONTACT (κ, μ)-MANIFOLDS

2008 ◽  
Vol 50 (3) ◽  
pp. 499-507 ◽  
Author(s):  
BENIAMINO CAPPELLETTI MONTANO ◽  
LUIGIA DI TERLIZZI ◽  
MUKUT MANI TRIPATHI
Keyword(s):  
Vector Field ◽  
Characteristic Vector ◽  
Invariant Submanifold ◽  
Totally Geodesic Submanifold ◽  
Totally Geodesic ◽  
Geodesic Submanifold ◽  
Invariant Submanifolds ◽  
Characteristic Vector Field

AbstractInvariant submanifolds of contact (κ, μ)-manifolds are studied. Our main result is that any invariant submanifold of a non-Sasakian contact (κ, μ)-manifold is always totally geodesic and, conversely, every totally geodesic submanifold of a non-Sasakian contact (κ, μ)-manifold, μ ≠ 0, such that the characteristic vector field is tangent to the submanifold is invariant. Some consequences of these results are then discussed.

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 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 Einstein null hypersurfaces of $(LCS)_{n+2}$-space forms

2019 ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Ricci Tensor ◽  
Null Hypersurface ◽  
Space Forms ◽  
Null Hypersurfaces ◽  
Geometric Conditions ◽  
Null Curves ◽  
Products Of Spheres

We show that ascreen null hypersurfaces of an $(n+2)$-dimensional Lorentzian concircular structure $(LCS)_{n+2}$-manifold admits an induced Ricci tensor. We, therefore, prove, under some geometric conditions, that an Einstein ascreen null hypersurface is locally a product of null curves and products of spheres.

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.

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