Geometric Inequalities of Warped Product Submanifolds and Their Applications

被引：2

作者：

Alluhaibi, Nadia ^{[1
]}

Mofarreh, Fatemah ^{[2
]}

Ali, Akram ^{[3
]}

Mior Othman, Wan Ainun ^{[4
]}

机构：

[1] King Abdulaziz Univ, Sci & Arts Coll, Dept Math, Rabigh Campus, Jeddah 21589, Saudi Arabia

[2] Princess Nourah bint Abdulrahman Univ, Fac Sci, Math Sci Dept, Riyadh 11546, Saudi Arabia

[3] King Khalid Univ, Coll Sci, Dept Math, Abha 62529, Saudi Arabia

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

来源：

MATHEMATICS | 2020年 / 8卷 / 05期

关键词：

warped product; sphere theorem; Laplacian; inequalities; diffeomorphic; ISOMETRIC IMMERSIONS; MINIMAL SUBMANIFOLDS; SPHERE; TOPOLOGY; THEOREMS; REAL;

D O I：

10.3390/math8050759

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, we prove that if Laplacian for the warping function of complete warped product submanifold M-m = B-p x(h) F-q in a unit sphere Sm+k satisfies some extrinsic inequalities depending on the dimensions of the base B-p and fiber F-q such that the base B-p is minimal, then M-m must be diffeomorphic to a unit sphere S-m. Moreover, we give some geometrical classification in terms of Euler-Lagrange equation and Hamiltonian of the warped function. We also discuss some related results.

引用

页数：11

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