scholarly journals Geometric inequality of warped product semi-slant submanifolds of locally product Riemannian manifolds

2019 ◽  
Vol 6 (1) ◽  
pp. 1602017
Author(s):  
Rifaqat Ali ◽  
Wan Ainun Mior Othman ◽  
Lishan Liu
Keyword(s):  
Riemannian Manifolds ◽  
Warped Product ◽  
Geometric Inequality ◽  
Slant Submanifolds

scholarly journals Types of Submanifolds in Metallic Riemannian Manifolds: A Short Survey

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2467
Author(s):  
Cristina E. Hretcanu ◽  
Adara M. Blaga
Keyword(s):  
Riemannian Manifolds ◽  
Warped Product ◽  
Slant Submanifolds ◽  
Short Survey ◽  
Existence And Nonexistence ◽  
Invariant Submanifolds

We provide a brief survey on the properties of submanifolds in metallic Riemannian manifolds. We focus on slant, semi-slant and hemi-slant submanifolds in metallic Riemannian manifolds and, in particular, on invariant, anti-invariant and semi-invariant submanifolds. We also describe the warped product bi-slant and, in particular, warped product semi-slant and warped product hemi-slant submanifolds in locally metallic Riemannian manifolds, obtaining some results regarding the existence and nonexistence of non-trivial semi-invariant, semi-slant and hemi-slant warped product submanifolds. We illustrate all these by suitable examples.

scholarly journals Warped Product Submanifolds in Locally Golden Riemannian Manifolds with a Slant Factor

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2125
Author(s):  
Cristina E. Hretcanu ◽  
Adara M. Blaga
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Euclidean Spaces ◽  
Slant Submanifolds

In the present paper, we study some properties of warped product pointwise semi-slant and hemi-slant submanifolds in Golden Riemannian manifolds, and we construct examples in Euclidean spaces. Additionally, we study some properties of proper warped product pointwise semi-slant (and, respectively, hemi-slant) submanifolds in a locally Golden Riemannian manifold.

Geometry of warped product pointwise semi-slant submanifolds of Kaehler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3771-3788 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Wan Othman
Keyword(s):  
Warped Product ◽  
Sufficient Conditions ◽  
Second Fundamental Form ◽  
Geometric Inequality ◽  
Tensor Fields ◽  
Space Forms ◽  
Kaehler Manifolds ◽  
Slant Submanifolds ◽  
Necessary And Sufficient ◽  
Complex Space Forms

In this paper, we study warped product pointwise semi-slant submanifolds of a Kaehler manifold. First, we prove some characterizations results in terms of the tensor fields T and F and then, we obtain a geometric inequality for the second fundamental form in terms of intrinsic invariants. Furthermore, the equality case is also discussed. Moreover, we give some applications for Riemannian and compact Remannian submanifolds as well, i.e., we construct necessary and sufficient conditions for the non-existence of compact warped product pointwise semi-slant submanifold in complex space forms.

scholarly journals Warped product pointwise pseudo-slant submanifolds of locally product Riemannian manifolds

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 423-438 ◽  
Author(s):  
Lamia Alqahtani ◽  
Siraj Uddina
Keyword(s):  
Riemannian Manifold ◽  
Fundamental Form ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Characterization Theorem ◽  
Second Fundamental Form ◽  
Warping Function ◽  
Equality Case ◽  
Slant Submanifolds ◽  
The Second Fundamental Form

In [3], it was shown that there are no warped product submanifolds of a locally product Riemannian manifold such that the spherical submanifold of a warped product is proper slant. In this paper, we introduce the notion of warped product submanifolds with a slant function and show that there exists a class of non-trivial warped product submanifolds of a locally product Riemannian manifold such that the spherical submanifold is pointwise slant by giving some examples. We present a characterization theorem and establish a sharp relationship between the squared norm of the second fundamental form and the warping function in terms of the slant function for such warped product submanifolds of a locally product Riemannian manifold. The equality case is also considered.

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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