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

Ali H. Alkhaldi, Pişcoran Laurian-Ioan*, Izhar Ahmad, Akram Ali

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish
Article number3884
Issue number20
StatePublished - Oct 2022

Bibliographical note

Funding Information:
The authors would like to express their gratitude to Deanship of Scientific Research at King Khalid University, Saudi Arabia for providing funding to the research group under the research grant R.G.P. 2/199/43.

Publisher Copyright:
© 2022 by the authors.


  • complex space form
  • Dirichlet energy
  • Homology groups
  • sphere theorem
  • stable currents
  • warped product submanifolds

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Mathematics (all)
  • Engineering (miscellaneous)


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