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.

scholarly journals Some Remarks on Quasi-Generalized CR-Null Geometry in Indefinite Nearly Cosymplectic Manifolds

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Fortuné Massamba ◽  
Samuel Ssekajja
Keyword(s):  
Totally Umbilical ◽  
Cosymplectic Manifold ◽  
Cosymplectic Manifolds ◽  
Nearly Cosymplectic ◽  
Geometric Effects

Attention is drawn to some distributions on ascreen Quasi-Generalized Cauchy-Riemannian (QGCR) null submanifolds in an indefinite nearly cosymplectic manifold. We characterize totally umbilical and irrotational ascreen QGCR-null submanifolds. We finally discuss the geometric effects of geodesity conditions on such submanifolds.

scholarly journals Pseudo-slant submanifolds in cosymplectic space forms

2016 ◽  
Vol 8 (1) ◽  
pp. 53-74 ◽  
Author(s):  
Süleyman Dirik ◽  
Mehmet Atçeken
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Slant Submanifold ◽  
Space Forms ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Cosymplectic Manifold ◽  
Slant Submanifolds ◽  
Cosymplectic Manifolds ◽  
Necessary And Sufficient

Abstract In this paper, we study the geometry of the pseudo-slant submanifolds of a cosymplectic space form. Necessary and sufficient conditions are given for a submanifold to be a pseudo-slant submanifold, pseudo-slant product, mixed geodesic and totally geodesic in cosymplectic manifolds. Finally, we give some results for totally umbilical pseudo-slant submanifold in a cosymplectic manifold and cosymplectic space form.

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 Warped Product Semi-Invariant Submanifolds of Nearly Cosymplectic Manifolds

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Siraj Uddin ◽  
S. H. Kon ◽  
M. A. Khan ◽  
Khushwant Singh
Keyword(s):  
Warped Product ◽  
Riemannian Product ◽  
Cosymplectic Manifold ◽  
Cosymplectic Manifolds ◽  
Invariant Submanifolds ◽  
Nearly Cosymplectic

We study warped product semi-invariant submanifolds of nearly cosymplectic manifolds. We prove that the warped product of the type is a usual Riemannian product of and , where and are anti-invariant and invariant submanifolds of a nearly cosymplectic manifold , respectively. Thus we consider the warped product of the type and obtain a characterization for such type of warped product.

scholarly journals Contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold

2013 ◽  
Vol 5 (2) ◽  
pp. 157-168
Author(s):  
Barnali Laha ◽  
Bandana Das ◽  
Arindam Bhattacharyya
Keyword(s):  
Sasakian Manifold ◽  
Invariant Distribution ◽  
Sasakian Manifolds ◽  
Totally Geodesic ◽  
Cr Submanifolds

Abstract In this paper we prove some properties of the indefinite Lorentzian para-Sasakian manifolds. Section 1 is introductory. In Section 2 we define D-totally geodesic and D⊥-totally geodesic contact CRsubmanifolds of an indefinite Lorentzian para-Sasakian manifold and deduce some results concerning such a manifold. In Section 3 we state and prove some results on mixed totally geodesic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold. Finally, in Section 4 we obtain a result on the anti-invariant distribution of totally umbilic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold.

scholarly journals Clairaut anti-invariant submersions from Lorentzian trans-Sasakian manifolds

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohd Danish Siddiqi ◽  
Shudhakar Kumar Chaubey ◽  
Aliya Naaz Siddiqui
Keyword(s):  
Sasakian Manifold ◽  
Fair Value ◽  
Geometrical Analysis ◽  
Sasakian Manifolds ◽  
Kenmotsu Manifold ◽  
Content Type ◽  
Research Article ◽  
Cosymplectic Manifolds ◽  
Necessary And Sufficient ◽  
Clairaut Submersion

PurposeThe central idea of this research article is to examine the characteristics of Clairaut submersions from Lorentzian trans-Sasakian manifolds of type (α, β) and also, to enhance this geometrical analysis with some specific cases, namely Clairaut submersion from Lorentzian α-Sasakian manifold, Lorentzian β-Kenmotsu manifold and Lorentzian cosymplectic manifold. Furthermore, the authors discuss some results about Clairaut Lagrangian submersions whose total space is a Lorentzian trans-Sasakian manifolds of type (α, β). Finally, the authors furnished some examples based on this study.Design/methodology/approachThis research discourse based on classifications of submersion, mainly Clairaut submersions, whose total manifolds is Lorentzian trans-Sasakian manifolds and its all classes like Lorentzian Sasakian, Lorenztian Kenmotsu and Lorentzian cosymplectic manifolds. In addition, the authors have explored some axioms of Clairaut Lorentzian submersions and illustrates our findings with some non-trivial examples.FindingsThe major finding of this study is to exhibit a necessary and sufficient condition for a submersions to be a Clairaut submersions and also find a condition for Clairaut Lagrangian submersions from Lorentzian trans-Sasakian manifolds.Originality/valueThe results and examples of the present manuscript are original. In addition, more general results with fair value and supportive examples are provided.

Nearly cosymplectic manifolds with nullity conditions

2019 ◽  
Vol 12 (06) ◽  
pp. 2040012 ◽  
Author(s):  
Mustafa Yıldırım ◽  
Gülhan Ayar
Keyword(s):  
Cosymplectic Manifold ◽  
Projectively Flat ◽  
Cosymplectic Manifolds ◽  
Nullity Distribution ◽  
Nearly Cosymplectic ◽  
Text Condition

We investigate nearly cosymplectic manifolds with [Formula: see text]-nullity distribution. Also, we consider pseudo-projectively flat [Formula: see text]-nearly cosymplectic manifold and study [Formula: see text] condition.

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 ON NON-INVARIANT HYPERSURFACES OF AN ε-PARA SASAKIAN MANIFOLD

2020 ◽  
Vol 35 (1) ◽  
pp. 001
Author(s):  
Shyam Kishor ◽  
Prerna Kanaujia
Keyword(s):  
Sasakian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Necessary And Sufficient ◽  
Induced Structure

In the present paper non-invariant hypersurfaces of an ε- para Sasakian manifold of an induced structure (f,g,u,v,λ) are studied. Some properties followed by this structure are obtained. A necessary and sufficient condition for totally umbilical non-invariant hypersurfaces equipped with (f,g,u,v,λ)- structure of ε-para Sasakian manifold to be totally geodesic has also been explored.

scholarly journals Totally Umbilical Proper Slant and Hemislant Submanifolds of an LP-Cosymplectic Manifold

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Siraj Uddin ◽  
Meraj Ali Khan ◽  
Khushwant Singh
Keyword(s):  
Present Note ◽  
Slant Submanifold ◽  
Slant Angle ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Cosymplectic Manifold ◽  
Integrability Conditions

In the present note, we study slant and hemislant submanifolds of an LP-cosymplectic manifold which are totally umbilical. We prove that every totally umbilical proper slant submanifoldMof an LP-cosymplectic manifoldM¯is either totally geodesic or ifMis not totally geodesic inM¯then we derive a formula for slant angle ofM. Also, we obtain the integrability conditions of the distributions of a hemi-slant submanifold, and then we give a result on its classification.

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