Characterizing Base in Warped Product Submanifolds of Complex Projective Spaces by Differential Equations

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this study, a link between the squared norm of the second fundamental form and the Laplacian of the warping function for a warped product pointwise semi-slant submanifold Mn in a complex projective space is presented. Some characterizations of the base NT of Mn are offered as applications. We also look at whether the base NT is isometric to the Euclidean space Rp or the Euclidean sphere Sp, subject to some constraints on the second fundamental form and warping function.

Original languageEnglish
Article number244
JournalMathematics
Volume10
Issue number2
DOIs
StatePublished - 1 Jan 2022

Bibliographical note

Funding Information:
Funding: The authors would like to express their gratitude to Deanship of Scientific Research at King Khalid University, Saudi Arabia for providing funding research group under the research grant R. G. P.1/135/42.

Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

  • Complex projective spaces
  • Dirichlet energy
  • Ordinary differential equations
  • Ricci curvature
  • Warped products

ASJC Scopus subject areas

  • Mathematics (all)

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