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

Autor:	Ali H. Alkhaldi, Pişcoran Laurian-Ioan, Izhar Ahmad, Akram Ali
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	warped product submanifolds complex space form Homology groups sphere theorem stable currents Dirichlet energy Mathematics QA1-939
Zdroj:	Mathematics, Vol 10, Iss 20, p 3884 (2022)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math10203884
Popis:	In this paper, we prove the nonexistence of stable integral currents in compact oriented warped product pointwise semi-slant submanifold Mn of a complex space form M˜(4ϵ) 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 Mn are vanished. As applications of homology groups, we derive new topological sphere theorems for warped product pointwise semi-slant submanifold Mn, in which Mn is homeomorphic to a sphere Sn if n≥4 and if n=3, then M3 is homotopic to a sphere S3 under the assumption of extrinsic conditions. Moreover, the same results are generalized for CR-warped product submanifolds.
Databáze:	Directory of Open Access Journals
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