scholarly journals Some properties of lightlike submanifolds of semi-Riemannian manifolds

2010 ◽  
Vol 43 (3) ◽  
Author(s):  
Rakesh Kumar ◽  
Rachna Rani ◽  
R. K. Nagaich
Keyword(s):  
Riemannian Manifolds ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Totally Geodesic ◽  
Screen Distribution ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

AbstractWe initially obtain various relations and then establish necessary and sufficient condition for the integrability of screen distribution of a lightlike submanifold. We also establish necessary and sufficient condition for a lightlike submanifold to be totally geodesic.

scholarly journals Anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1429-1444 ◽  
Author(s):  
Cengizhan Murathan ◽  
Erken Küpeli
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Submersion ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Cosymplectic Manifolds ◽  
Necessary And Sufficient ◽  
Decomposition Theorems ◽  
Characteristic Vector Field

We introduce anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on cosymplectic manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and harmonic. We give examples of anti-invariant submersions such that characteristic vector field ? is vertical or horizontal. Moreover we give decomposition theorems by using the existence of anti-invariant Riemannian submersions.

Radical screen transversal lightlike submanifolds of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection

2018 ◽  
Vol 15 (02) ◽  
pp. 1850024
Author(s):  
Garima Gupta ◽  
Rakesh Kumar ◽  
Rakesh Kumar Nagaich
Keyword(s):  
Product Manifold ◽  
Necessary And Sufficient Condition ◽  
Kaehler Manifold ◽  
Screen Distribution ◽  
Kaehler Manifolds ◽  
Metric Connection ◽  
Necessary And Sufficient ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We study radical screen transversal ([Formula: see text])-lightlike submanifolds of an indefinite Kaehler manifold admitting a quarter-symmetric non-metric connection and obtain a necessary and sufficient condition for the screen distribution of a radical [Formula: see text]-lightlike submanifold to be integrable. We also study totally umbilical radical [Formula: see text]-lightlike submanifolds and obtain some characterization theorems for a radical [Formula: see text]-lightlike submanifold to be a lightlike product manifold. Finally, we establish some results regarding the vanishes of null sectional curvature.

scholarly journals Anti-invariant Riemanian submersions from nearly-k-cosymplectic manifolds

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1159-1174
Author(s):  
Ju Tan ◽  
Na Xu
Keyword(s):  
Vector Field ◽  
Riemannian Manifolds ◽  
Riemannian Submersion ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Cosymplectic Manifolds ◽  
Necessary And Sufficient ◽  
Characteristic Vector Field

In this paper, we introduce anti-invariant Riemannian submersions from nearly-K-cosymplectic manifolds onto Riemannian manifolds. We study the integrability of horizontal distributions. And we investigate the necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and harmonic. Moreover, we give examples of anti-invariant Riemannian submersions such that characteristic vector field ? is vertical or horizontal.

Geometry of semi-transversal lightlike warped product submanifolds of indefinite Kaehler manifolds

2019 ◽  
pp. 2150001
Author(s):  
Sangeet Kumar
Keyword(s):  
Warped Product ◽  
Shape Operator ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Kaehler Manifold ◽  
Type Formula ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

In this paper, we investigate warped product semi-transversal lightlike submanifolds of indefinite Kaehler manifolds. It is shown that there does not exist any warped product semi-transversal lightlike submanifold of the type [Formula: see text] in an indefinite Kaehler manifold. Moreover, a necessary and sufficient condition for an isometrically immersed semi-transversal lightlike submanifold of an indefinite Kaehler manifold to be a semi-transversal lightlike warped product of the type [Formula: see text] is obtained, in terms of the shape operator.

scholarly journals On Totally Contact Umbilical Contact CR-Lightlike Submanifolds Of Indefinite Sasakian Manifolds

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Manish Gogna ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sasakian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

AbstractAfter brief introduction, we prove that a totally contact umbilical CR- lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold. Finally, we characterize a contact CR-lightlike submanifold of indefinite Sasakian manifold to be a contact CR-lightlike product

scholarly journals Bakry-Émery Conditions on Almost Smooth Metric Measure Spaces

2018 ◽  
Vol 6 (1) ◽  
pp. 129-145 ◽  
Author(s):  
Shouhei Honda
Keyword(s):  
Riemannian Manifolds ◽  
Short Note ◽  
Sufficient Condition ◽  
Metric Measure Spaces ◽  
Necessary And Sufficient Condition ◽  
Local Dimension ◽  
Base Points ◽  
Smooth Metric Measure Spaces ◽  
Measure Spaces ◽  
Necessary And Sufficient

Abstract In this short note, we give a sufficient condition for almost smooth compact metric measure spaces to satisfy the Bakry-Émery condition BE(K, N). The sufficient condition is satisfied for the glued space of any two (not necessary same dimensional) closed pointed Riemannian manifolds at their base points. This tells us that the BE condition is strictly weaker than the RCD condition even in this setting, and that the local dimension is not constant even if the space satisfies the BE condition with the coincidence between the induced distance by the Cheeger energy and the original distance. In particular, the glued space gives a first example with a Ricci bound from below in the Bakry-Émery sense, whose local dimension is not constant. We also give a necessary and sufficient condition for such spaces to be RCD(K, N) spaces.

scholarly journals Anti-invariant Riemannian submersions from nearly Kaehler manifolds

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1219-1235 ◽  
Author(s):  
Shahid Ali ◽  
Tanveer Fatima
Keyword(s):  
Riemannian Submersion ◽  
Horizontal Distribution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Decomposition Theorems ◽  
The Vertical Distribution

We extend the notion of anti-invariant and Langrangian Riemannian submersion to the case when the total manifold is nearly Kaehler. We obtain the integrability conditions for the horizontal distribution while it is noted that the vertical distribution is always integrable. We also investigate the geometry of the foliations of the two distributions and obtain the necessary and sufficient condition for a Langrangian submersion to be totally geodesic. The decomposition theorems for the total manifold of the submersion are obtained.

scholarly journals On the Differential Equation Governing Torqued Vector Fields on a Riemannian Manifold

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1941
Author(s):  
Sharief Deshmukh ◽  
Nasser Bin Turki ◽  
Haila Alodan
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Euclidean Space ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Compact Riemannian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Rigidity Results ◽  
Necessary And Sufficient

In this article, we show that the presence of a torqued vector field on a Riemannian manifold can be used to obtain rigidity results for Riemannian manifolds of constant curvature. More precisely, we show that there is no torqued vector field on n-sphere Sn(c). A nontrivial example of torqued vector field is constructed on an open subset of the Euclidean space En whose torqued function and torqued form are nowhere zero. It is shown that owing to topology of the Euclidean space En, this type of torqued vector fields could not be extended globally to En. Finally, we find a necessary and sufficient condition for a torqued vector field on a compact Riemannian manifold to be a concircular vector field.

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.

TOTALLY GEODESIC SUBMANIFOLDS OF GL-MANIFOLDS

2012 ◽  
Vol 09 (01) ◽  
pp. 1250002
Author(s):  
ABOLGHASEM LALEH ◽  
MORTEZA M. REZAII ◽  
ATAABAK BAAGHERZADEH HUSHMANDI
Keyword(s):  
Riemannian Manifold ◽  
Finsler Manifold ◽  
Finsler Metric ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Totally Geodesic ◽  
Geodesic Submanifolds ◽  
Totally Geodesic Submanifolds ◽  
Necessary And Sufficient ◽  
Sasakian Metric

In this paper, for a Finsler manifold (M, F) with a Finsler metric gij(x, y) we shall consider a generalized Lagrange metrics (FGL-metrics) as the form *gij(x, y) = gij(x, y) + σ(x, y)Bi(x, y)Bj(x, y) on TM. Then we shall consider a Riemannian manifold (TM, *G) in which *G is a generalized Sasakian metric of *g on [Formula: see text]. Then we restrict the above FGL-metrics to a submanifold of [Formula: see text], and show that it admits a GL-metric structure. Then we shall find a necessary and sufficient condition for this submanifold to be totally geodesic.

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