Abstract
In this paper, we prove the nonexistence of stable integral currents in compact oriented warped product pointwise semi-slant submanifold (Formula presented.) of a complex space form (Formula presented.) 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 (Formula presented.) are vanished. As applications of homology groups, we derive new topological sphere theorems for warped product pointwise semi-slant submanifold (Formula presented.), in which (Formula presented.) is homeomorphic to a sphere (Formula presented.) if (Formula presented.) and if (Formula presented.), then (Formula presented.) is homotopic to a sphere (Formula presented.) under the assumption of extrinsic conditions. Moreover, the same results are generalized for CR-warped product submanifolds.
| Original language | English |
|---|---|
| Article number | 3884 |
| Journal | Mathematics |
| Volume | 10 |
| Issue number | 20 |
| DOIs | |
| State | Published - Oct 2022 |
Bibliographical note
Publisher Copyright:© 2022 by the authors.
Keywords
- Dirichlet energy
- Homology groups
- complex space form
- sphere theorem
- stable currents
- warped product submanifolds
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- General Mathematics
- Engineering (miscellaneous)