Geometry of warped product immersions of Kenmotsu space forms and its applications to slant immersions

JOURNAL OF GEOMETRY AND PHYSICS

卷:114

Article

Ali, Akram¹  Piscoran, Laurian-Ioan² 

[1] Univ Malaya, Inst Math Sci, Fac Sci, Kuala Lumpur 50603, Malaysia

[2] Tech Univ Cluj Napoca, North Univ Ctr Baia Mare, Dept Math & Comp Sci, Victoriei 76, Baia Mare 430122, Romania

关键词: Warped products;    Semi-slant immersions;    Connected;    Compact Riemannian submanifolds;    Kenmotsu space forms;    Hamiltonian;    Kinetic energy;   

DOI  :  10.1016/j.geomphys.2016.12.001

来源: Elsevier

【 摘 要 】

In this paper, some relations among the second fundamental form which is an extrinsic invariant, Laplacian of the warping function and constant sectional curvature of a warped product semi-slant submanifold of a Kenmotsu space form and its totally geodesic and totally umbilical submanifolds are described from the exploitation of the Gauss equation instead of the Codazzi equation in the sense of Chen's studies in (2003). These relations provide us an approach to the classifications of equalities by the following case studied of Hasegawa and Mihai (2003). These are exemplified by the classifications of the totally geodesic and totally umbilical submanifolds. Moreover, we provide some applications of the inequality case by using the harrnonicity of the smooth warping functions. In particular, we prove the triviality of connected, compact warped product semi-slant manifolds isometrically immersed into a Kenmotsu space form using Hamiltonian, Hessian, and the Kinetic energy of the warped function. Further, we generalize some results for contact CR-warped products in a Kenmotsu space form. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free