scholarly journals Warped Product Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Siraj Uddin ◽  
Bernardine R. Wong ◽  
A. A. Mustafa
Keyword(s):  
Warped Product ◽  
Cosymplectic Manifold ◽  
Slant Submanifolds ◽  
Nearly Cosymplectic

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 A note on warped product submanifolds of cosymplectic manifolds

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 95-102 ◽  
Author(s):  
Siraj Uddin ◽  
V.A. Khan ◽  
K.A. Khan
Keyword(s):  
Warped Product ◽  
Warped Products ◽  
Cosymplectic Manifold ◽  
Slant Submanifolds ◽  
Cosymplectic Manifolds

In this paper, we study warped product anti-slant submanifolds of cosymplectic manifolds. It is shown that the cosymplectic manifold do not admit non trivial warped product submanifolds in the form N??f N? and then we obtain some results for the existence of warped products of the type N??f N?, where N? and N? are anti-invariant and proper slant submanifolds of a cosymplectic manifold M?, respectively.

Pointwise pseudo-slant submanifolds of a Kenmotsu manifold

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5833-5853 ◽  
Author(s):  
Viqar Khan ◽  
Mohammad Shuaib
Keyword(s):  
Present Article ◽  
Warped Product ◽  
Shape Operator ◽  
Warped Products ◽  
Canonical Structure ◽  
Slant Submanifold ◽  
Kenmotsu Manifold ◽  
Slant Submanifolds ◽  
Kenmotsu Manifolds

In the present article, we have investigated pointwise pseudo-slant submanifolds of Kenmotsu manifolds and have sought conditions under which these submanifolds are warped products. To this end first, it is shown that these submanifolds can not be expressed as non-trivial doubly warped product submanifolds. However, as there exist non-trivial (single) warped product submanifolds of a Kenmotsu manifold, we have worked out characterizations in terms of a canonical structure T and the shape operator under which a pointwise pseudo slant submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

scholarly journals RETRACTED Warped Product Pointwise Semi-slant Submanifolds of Sasakian Manifol Retracted

2021 ◽  
Vol 45 (5) ◽  
pp. 721-738
Author(s):  
ION MIHAI ◽  
◽  
SIRAJ UDDIN ◽  
АДЕЛА MIHAI
Keyword(s):  
Warped Product ◽  
Warped Products ◽  
Sasakian Manifolds ◽  
Slant Submanifolds ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds

Recently, B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using the notion of pointwise slant submanifolds, we investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian manifolds. We give non-trivial examples of such submanifolds and obtain several fundamental results, including a characterization for warped product pointwise semi-slant submanifolds of Sasakian manifolds.

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 Warped Product Submanifolds of LP-Sasakian Manifolds

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
S. K. Hui ◽  
S. Uddin ◽  
C. Özel ◽  
A. A. Mustafa
Keyword(s):  
Warped Product ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Slant Submanifolds

We study of warped product submanifolds, especially warped product hemi-slant submanifolds of LP-Sasakian manifolds. We obtain the results on the nonexistance or existence of warped product hemi-slant submanifolds and give some examples of LP-Sasakian manifolds. The existence of warped product hemi-slant submanifolds of an LP-Sasakian manifold is also ensured by an interesting example.

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