Classification of Warped Product Submanifolds in Kenmotsu Space Forms Admitting Gradient Ricci Solitons

Ali H. Alkhaldi and Akram Ali
Additional contact information
Ali H. Alkhaldi: Department of Mathematics, College of Science, King Khalid University, 9004 Abha, Saudi Arabia
Akram Ali: Department of Mathematics, College of Science, King Khalid University, 9004 Abha, Saudi Arabia

Mathematics, 2019, vol. 7, issue 2, 1-11

Abstract: The purpose of this article is to obtain geometric conditions in terms of gradient Ricci curvature, both necessary and sufficient, for a warped product semi-slant in a Kenmotsu space form, to be either CR-warped product or simply a Riemannian product manifold when a basic inequality become equality. The next purpose of this paper to find the necessary condition admitting gradient Ricci soliton, that the warped product semi-slant submanifold of Kenmotsu space form, is an Einstein warped product. We also discuss some obstructions to these constructions in more detail.

Keywords: warped products; Kenmotsu space forms; Euler-Lagrange equation; Ricci curvature; gradient Ricci soliton; gradient Ricci soliton warped product (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/2/112/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/2/112/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:2:p:112-:d:199792

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().