Hypersurfaces in nearly Kaehler manifold $$\pmb {\mathbb {S}}^{\varvec{3}}\varvec{\times } \pmb {\mathbb {S}}^{\varvec{3}}$$ S 3 × S 3

2017 ◽  
Vol 127 (4) ◽  
pp. 707-717
Author(s):  
Biaogui Yang ◽  
Qingqing Zhu
Keyword(s):  
Kaehler Manifold ◽  
Nearly Kaehler Manifold

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.

scholarly journals TOTALLY UMBILICAL CR-SUBMANIFOLDS OF A NEARLY KAEHLER MANIFOLD

1996 ◽  
Vol 27 (2) ◽  
pp. 145-149
Author(s):  
S. H. KON ◽  
SIN-LENG TAN
Keyword(s):  
Kaehler Manifold ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Cr Submanifold ◽  
Nearly Kaehler Manifold ◽  
Totally Real ◽  
Cr Submanifolds

The geometry of a CR-submanifold in a Kaehler manifold has been extensively studied. B.Y . Chen has classified the totally umbilical CR-submanifolds of a Kaehler manifold and showed that they are either totally geodesic, or totally real or dim$(D^{\perp}) =1$. In this paper we show that such a result is also true in a 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.

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.

scholarly journals Generic Submanifolds of Nearly Kaehler Manifolds with Certain Parallel Canonical Structure

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Qingqing Zhu ◽  
Biaogui Yang
Keyword(s):  
Point Of View ◽  
Real Hypersurfaces ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Generic Submanifolds ◽  
Geometric Point ◽  
Complex Submanifolds ◽  
Generic Submanifold ◽  
Nearly Kaehler Manifold ◽  
Totally Real

The class of generic submanifold includes all real hypersurfaces, complex submanifolds, totally real submanifolds, and CR-submanifolds. In this paper we initiate the study of generic submanifolds in a nearly Kaehler manifold from differential geometric point of view. Some fundamental results in this paper will be obtained.

Hemi-slant submanifolds as warped products in a nearly Kaehler manifold

2017 ◽  
Vol 67 (3) ◽  
Author(s):  
Viqar Azam Khan ◽  
Kamran Khan
Keyword(s):  
Present Article ◽  
Warped Product ◽  
Warped Products ◽  
Kaehler Manifold ◽  
Slant Submanifold ◽  
Slant Submanifolds ◽  
Nearly Kaehler Manifold

AbstractThe present article is devoted to the study of conditions on a hemi-slant submanifold of a nearly Kaehler manifold under which the submanifold is a warped product submanifold.

A note on derived connections from semi-symmetric metric connections

2017 ◽  
Vol 67 (1) ◽  
pp. 221-226
Author(s):  
Adela Mihai
Keyword(s):  
Open Problem ◽  
Complex Structure ◽  
Kaehler Manifold ◽  
Different Types ◽  
Metric Connection

Abstract In this paper we construct examples of different types of connections starting from a semi-symmetric metric connection g, for example a connection which is a symmetric metric connection with respect to a conformally related metric, but symmetric non-metric with respect to the initial metric. We formulate an open problem: to find a parallel complex structure on a Kaehler manifold with respect to such a new connection.

scholarly journals Semi-invariant Riemannian submersions from nearly Kaehler manifolds

2020 ◽  
Vol 17 (07) ◽  
pp. 2050100
Author(s):  
Rupali Kaushal ◽  
Rashmi Sachdeva ◽  
Rakesh Kumar ◽  
Rakesh Kumar Nagaich
Keyword(s):  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Horizontal Distribution ◽  
Product Manifold ◽  
Riemannian Submersions ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Nearly Kaehler Manifold ◽  
The Vertical Distribution ◽  
Usual Product

We study semi-invariant Riemannian submersions from a nearly Kaehler manifold to a Riemannian manifold. It is well known that the vertical distribution of a Riemannian submersion is always integrable therefore, we derive condition for the integrability of horizontal distribution of a semi-invariant Riemannian submersion and also investigate the geometry of the foliations. We discuss the existence and nonexistence of semi-invariant submersions such that the total manifold is a usual product manifold or a twisted product manifold. We establish necessary and sufficient conditions for a semi-invariant submersion to be a totally geodesic map. Finally, we study semi-invariant submersions with totally umbilical fibers.

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