Estimation of inequalities for warped product semi-slant submanifolds of Kenmotsu space forms

Misbah Liaqat,Wan Ainun Mior Othman,Akram Ali,Piscoran Laurian-Ioan,Abdullah Gani,Cenap Ozel

doi:10.1186/s13660-016-1177-y

Misbah Liaqat, Wan Ainun Mior Othman + Show 4 more

Open Access

https://doi.org/10.1186/s13660-016-1177-y

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Abstract

In this paper, we construct the geometric inequalities for the squared norm of the mean curvature and warping functions of warped product semi-slant submanifolds in Kenmotsu space forms. The equality cases are also discussed.

Highlights

The theory of warped product manifolds is an emerging research area in differential geometry
Uddin in [ ] and Srivastava in [ ] proved that the warped product semi-slant submanifold of a Kenmotsu manifold exists in the forms M = MT ×f Mθ and M = Mθ ×f MT, except in the case when the structure vector field ξ is tangent to MT and Mθ, respectively
3 Main inequalities as applications of very famous studied of Nolker in [ ], we obtain the following inequality for warped product semi-slant submanifolds of Kenmotsu space form such that ξ is tangent to the first factor of the warped product, i.e., we have the following

Summary

Introduction

The theory of warped product manifolds is an emerging research area in differential geometry. Let φ : M ×f M be an isometrically immersion of an n-dimensional warped product into m-dimensional real space form M(c) with constant sectional curvature c.

Results

Conclusion