Vanishing Homology of Warped Product Submanifolds in Complex Space Forms and Applications

Ali H. Alkhaldi, Pişcoran Laurian-Ioan (), Izhar Ahmad and Akram Ali
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Ali H. Alkhaldi: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Pişcoran Laurian-Ioan: Department of Mathematics and Computer Science Victoriei 76, North Center of Baia Mare Technical University of Cluj Napoca, 430122 Baia Mare, Romania
Izhar Ahmad: Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Akram Ali: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia

Mathematics, 2022, vol. 10, issue 20, 1-17

Abstract: In this paper, we prove the nonexistence of stable integral currents in compact oriented warped product pointwise semi-slant submanifold M n of a complex space form M ˜ ( 4 ϵ ) under extrinsic conditions which involve the Laplacian, the squared norm gradient of the warped function, and pointwise slant functions. We show that i -the homology groups of M n are vanished. As applications of homology groups, we derive new topological sphere theorems for warped product pointwise semi-slant submanifold M n , in which M n is homeomorphic to a sphere S n if n ≥ 4 and if n = 3 , then M 3 is homotopic to a sphere S 3 under the assumption of extrinsic conditions. Moreover, the same results are generalized for CR-warped product submanifolds.

Keywords: warped product submanifolds; complex space form; Homology groups; sphere theorem; stable currents; Dirichlet energy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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