Some characterization theorems on GCR-lightlike warped product submanifolds of indefinite nearly Kaehler manifolds

2020 ◽  
Vol 17 (03) ◽  
pp. 2050039
Author(s):  
Sangeet Kumar
Keyword(s):  
Warped Product ◽  
Shape Operator ◽  
Kaehler Manifold ◽  
Type Formula ◽  
Kaehler Manifolds ◽  
Metric Connection ◽  
Characterization Theorems ◽  
Nearly Kaehler Manifold ◽  
Totally Geodesic Foliation ◽  
Lightlike Submanifold

It is shown that for a proper Generalized Cauchy–Riemann ([Formula: see text])-lightlike submanifold of an indefinite nearly Kaehler manifold such that [Formula: see text] defines a totally geodesic foliation in [Formula: see text], there does not exist any warped product [Formula: see text]-lightlike submanifold of the type [Formula: see text]. Then, the existence of [Formula: see text]-lightlike warped product submanifolds of the type [Formula: see text] in indefinite nearly Kaehler manifolds is obtained by establishing a characterization in terms of the shape operator. Further, we prove that for a proper [Formula: see text]-lightlike warped product submanifold of an indefinite nearly Kaehler manifold, the induced connection [Formula: see text] can never be a metric connection. Finally, we derive some characterizations in terms of the canonical structures [Formula: see text] and [Formula: see text] on a [Formula: see text]-lightlike submanifold of an indefinite nearly Kaehler manifold enabling it to be a [Formula: see text]-lightlike warped product.

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.

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.

Some results on normal GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds

2019 ◽  
Vol 16 (03) ◽  
pp. 1950037
Author(s):  
Megha ◽  
Sangeet Kumar
Keyword(s):  
Sufficient Conditions ◽  
Characterization Theorem ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Holomorphic Bisectional Curvature ◽  
Necessary And Sufficient ◽  
Nearly Kaehler Manifold ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold ◽  
Normal Formula

The purpose of this paper is to study normal [Formula: see text]-lightlike submanifolds of indefinite nearly Kaehler manifolds. We find some necessary and sufficient conditions for an isometrically immersed [Formula: see text]-lightlike submanifold of an indefinite nearly Kaehler manifold to be a normal [Formula: see text]-lightlike submanifold. Further, we derive a characterization theorem for holomorphic bisectional curvature of a normal [Formula: see text]-lightlike submanifold of an indefinite nearly Kaehler manifold.

Geometric classification of warped product submanifolds of nearly Kaehler manifolds with a slant fiber

2019 ◽  
Vol 16 (02) ◽  
pp. 1950031 ◽  
Author(s):  
Akram Ali ◽  
Jae Won Lee ◽  
Ali H. Alkhaldi
Keyword(s):  
Warped Product ◽  
Second Fundamental Form ◽  
Warping Function ◽  
Kaehler Manifold ◽  
Slant Submanifold ◽  
Riemannian Product ◽  
Slant Angle ◽  
Kaehler Manifolds ◽  
Nearly Kaehler Manifold ◽  
Totally Real

There are two types of warped product pseudo-slant submanifolds, [Formula: see text] and [Formula: see text], in a nearly Kaehler manifold. We derive an optimization for an extrinsic invariant, the squared norm of second fundamental form, on a nontrivial warped product pseudo-slant submanifold [Formula: see text] in a nearly Kaehler manifold in terms of a warping function and a slant angle when the fiber [Formula: see text] is a slant submanifold. Moreover, the equality is verified for depending on what [Formula: see text] and [Formula: see text] are, and also we show that if the equality holds, then [Formula: see text] is a simply Riemannian product. As applications, we prove that the warped product pseudo-slant submanifold has the finite Kinetic energy if and only if [Formula: see text] is a totally real warped product submanifold.

scholarly journals Warped product semi-slant submanifolds in locally conformal Kaehler manifolds

2017 ◽  
Vol 10 (2) ◽  
Author(s):  
Koji Matsumoto
Keyword(s):  
Warped Product ◽  
Sufficient Conditions ◽  
Hermitian Manifold ◽  
Kaehler Manifold ◽  
Slant Submanifold ◽  
Kaehler Manifolds ◽  
Slant Submanifolds ◽  
Necessary And Sufficient ◽  
Locally Conformal ◽  
Nearly Kaehler Manifold

In 1994, in [13], N. Papaghiuc introduced the notion of semi-slant submanifold in a Hermitian manifold which is a generalization of CR- and slant-submanifolds. In particular, he considered this submanifold in Kaehlerian manifolds, [13]. Then, in 2007, V. A. Khan and M. A. Khan considered this submanifold in a nearly Kaehler manifold and obtained interesting results, [11]. Recently, we considered semi-slant submanifolds in a locally conformal Kaehler manifold and gave a necessary and sufficient conditions for two distributions (holomorphic and slant) to be integrable. Moreover, we considered these submanifolds in a locally conformal Kaehler space form, [4]. In this paper, we define 2-kind warped product semi-slant submanifolds in a locally conformal Kaehler manifold and consider some properties of these submanifolds.

scholarly journals Characterization of CR-Lightlike-Warped Product of Indefinite Kaehler Manifolds

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Rachna Rani ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Warped Product ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Lightlike Submanifold

In this paper, we prove that there does not exist a warped product CR-lightlike submanifold in the form other than CR-lightlike product in an indefinite Kaehler manifold. We also obtain some characterizations for a CR-lightlike submanifold to be locally a CR-lightlike warped product.

scholarly journals Geometric Mechanics on Warped Product Semi-Slant Submanifold of Generalized Complex Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Yanlin Li ◽  
Ali H. Alkhaldi ◽  
Akram Ali
Keyword(s):  
Warped Product ◽  
Complex Space ◽  
Slant Submanifold ◽  
Codazzi Equation ◽  
Space Forms ◽  
Kaehler Manifolds ◽  
Slant Submanifolds ◽  
Generalized Complex ◽  
Complex Space Forms ◽  
Nearly Kaehler Manifold

In this study, we develop a general inequality for warped product semi-slant submanifolds of type M n = N T n 1 × f N ϑ n 2 in a nearly Kaehler manifold and generalized complex space forms using the Gauss equation instead of the Codazzi equation. There are several applications that can be developed from this. It is also described how to classify warped product semi-slant submanifolds that satisfy the equality cases of inequalities (determined using boundary conditions). Several results for connected, compact warped product semi-slant submanifolds of nearly Kaehler manifolds are obtained, and they are derived in the context of the Hamiltonian, Dirichlet energy function, gradient Ricci curvature, and nonzero eigenvalue of the Laplacian of the warping functions.

scholarly journals Integrability of distributions in CR-lightlike submanifolds

2002 ◽  
Vol 33 (3) ◽  
pp. 209-222
Author(s):  
Bayram Sahin ◽  
Rifat Gunes
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

In this paper, we study CR-lighlike submanifolds of an indefinite Kaehler manifold. Integrability of distributions on CR-lightlike submanifold investigated. We give some necessary and sufficient conditions on integrability of distibutions on CR-lightlike submanifolds in an indefinite Kaehler manifolds.

scholarly journals Hemi-Slant Lightlike Submanifolds of Indefinite Kenmotsu Manifolds

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
S. M. Khursheed Haider ◽  
Mamta Thakur ◽  
Advin
Keyword(s):  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Metric Connection ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We introduce and study hemi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. We give an example of hemi-slant lightlike submanifold and establish two characterization theorems for the existence of such submanifolds. We prove some theorems which ensure the existence of minimal hemi-slant lightlike submanifolds and obtain a condition under which the induced connection ∇ on M is a metric connection. An example of proper minimal hemi-slant lightlike submanifolds is also given.

scholarly journals Radical screen transversal slant lightlike submanfolds of indefinite Kaehler manifolds

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 2037-2046
Author(s):  
Mamta Thakur ◽  
A Advin ◽  
S.M.K. Haider
Keyword(s):  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Characterization Theorems ◽  
Lightlike Submanifolds

In this paper, we define Radical screen transversal slant lightlike submanifolds of an indefinite Kaehler manifold and give an example. We prove two characterization theorems for the existence of the Radical screen transversal slant lightlike submanifolds and obtain the necessary and su_cient conditions for Radical screen transversal slant lightlike submanifolds to be Radical screen slant lightlike product.

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