On the Topology of Warped Product Pointwise Semi-Slant Submanifolds with Positive Curvature

Yanlin Li, Ali H. Alkhaldi, Akram Ali and Pişcoran Laurian-Ioan
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Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Ali H. Alkhaldi: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Akram Ali: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Pişcoran Laurian-Ioan: Department of Mathematics and Computer Science, North University Center of Baia Mare, Technical University of Cluj Napoca, 430122 Baia Mare, Romania

Mathematics, 2021, vol. 9, issue 24, 1-13

Abstract: In this paper, we obtain some topological characterizations for the warping function of a warped product pointwise semi-slant submanifold of the form Ω n = N T l × f N ϕ k in a complex projective space C P 2 m ( 4 ) . Additionally, we will find certain restrictions on the warping function f , Dirichlet energy function E ( f ) , and first non-zero eigenvalue λ 1 to prove that stable l -currents do not exist and also that the homology groups have vanished in Ω n . As an application of the non-existence of the stable currents in Ω n , we show that the fundamental group π 1 ( Ω n ) is trivial and Ω n is simply connected under the same extrinsic conditions. Further, some similar conclusions are provided for CR-warped product submanifolds.

Keywords: warped product submanifolds; complex projective spaces; homology groups; homotopy; sphere theorems; stable currents; kinetic energy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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