scholarly journals Totally umbilical semi-invariant submanifolds of a nearly Sasakian manifold

2008 ◽  
pp. 19-24
Author(s):  
Khalid Khan ◽  
S Siraj-Uddin ◽  
Nargis Jamal
Keyword(s):  
Sasakian Manifold ◽  
Totally Umbilical ◽  
Invariant Submanifolds ◽  
Nearly Sasakian

scholarly journals TOTALLY UMBILICAL SEMI-INVARIANT SUBMANIFOLDS AND CR-SUBMANIFOLDS OF A SASAKIAN MANIFOLD

1993 ◽  
Vol 24 (2) ◽  
pp. 161-172
Author(s):  
S. M. KHURSEED HAIDER ◽  
V. A. KHAN ◽  
S. I. HUSAIN
Keyword(s):  
Space Form ◽  
Sasakian Manifold ◽  
Classification Theorem ◽  
Sasakian Space Form ◽  
Invariant Submanifold ◽  
Totally Umbilical ◽  
Cr Submanifold ◽  
Invariant Submanifolds ◽  
Cr Submanifolds

In the present paper, a classification theorem for totally um- bilical semi-invariant submanifold is established. CR-submanifolds of a Sasakian space form are studied in detail, and finally a theorem for a CR- submanifold of a Sasakian manifold to be a proper contact CR-product is proved.

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 Infinitesimal variations of invariant submanifolds of a Sasakian manifold

1978 ◽  
Vol 1 (2) ◽  
pp. 219-236 ◽  
Author(s):  
Kentaro Yano ◽  
U-Hang Ki ◽  
Jin Suk Pak
Keyword(s):  
Sasakian Manifold ◽  
Invariant Submanifolds

On non-invariant hypersurfaces of a nearly hyperbolic Sasakian manifold

2017 ◽  
Vol 28 (08) ◽  
pp. 1750064
Author(s):  
Mobin Ahmad ◽  
Shadab Ahmad Khan ◽  
Toukeer Khan
Keyword(s):  
Fundamental Form ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Second Fundamental Form ◽  
Text Structure ◽  
Necessary And Sufficient Conditions ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
The Second Fundamental Form ◽  
Necessary And Sufficient

We consider a nearly hyperbolic Sasakian manifold equipped with [Formula: see text]-structure and study non-invariant hypersurface of a nearly hyperbolic Sasakian manifold equipped with [Formula: see text]-structure. We obtain some properties of nearly hyperbolic Sasakian manifold equipped with [Formula: see text]-structure. Further, we find the necessary and sufficient conditions for totally umbilical non-invariant hypersurface with [Formula: see text]-structure of nearly hyperbolic Sasakian manifold to be totally geodesic. We also calculate the second fundamental form of a non-invariant hypersurface of a nearly hyperbolic Sasakian manifold with [Formula: see text]-structure under the condition when f is parallel.

scholarly journals Noninvariant Hypersurfaces of a Nearly Trans-Sasakian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Satya Prakash Yadav ◽  
Shyam Kishor
Keyword(s):  
Contact Structure ◽  
Sasakian Manifold ◽  
Necessary Condition ◽  
Sasakian Manifolds ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Cosymplectic Manifold ◽  
Cosymplectic Manifolds ◽  
Nearly Cosymplectic

The present paper focuses on the study of noninvariant hypersurfaces of a nearly trans-Sasakian manifold equipped with(f,g,u,v,λ)-structure. Initially some properties of this structure have been discussed. Further, the second fundamental forms of noninvariant hypersurfaces of nearly trans-Sasakian manifolds and nearly cosymplectic manifolds with(f,g,u,v,λ)-structure have been calculated providedfis parallel. In addition, the eigenvalues offhave been found and proved that a noninvariant hypersurface with(f,g,u,v,λ)-structure of nearly cosymplectic manifold with contact structure becomes totally geodesic. Finally the paper has been concluded by investigating the necessary condition for totally geodesic or totally umbilical noninvariant hypersurface with(f,g,u,v,λ)-structure of a nearly trans-Sasakian manifold.

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