Geometric Inequalities of Warped Product Submanifolds and Their Applications

Nadia Alluhaibi, Fatemah Mofarreh, Akram Ali and Wan Ainun Mior Othman
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Nadia Alluhaibi: Department of Mathematics, Science and Arts College, Rabigh Campus, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Fatemah Mofarreh: Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia
Akram Ali: Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
Wan Ainun Mior Othman: Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia

Mathematics, 2020, vol. 8, issue 5, 1-11

Abstract: In the present paper, we prove that if Laplacian for the warping function of complete warped product submanifold M m = B p × h F q in a unit sphere S m + 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.

Keywords: warped product; sphere theorem; Laplacian; inequalities; diffeomorphic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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