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Invariant submanifolds of generalized Sasakian-space-forms

Shyamal Kumar Hui

http://orcid.org/0000-0001-5224-3467

Department of Mathematics, The University of Burdwan, Golapbag, Burdwan 713104, West Bengal, India

E-mail Address: skhui@math.buruniv.ac.in

Corresponding author.

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Siraj Uddin

Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

E-mail Address: siraj.ch@gmail.com

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ALi H. Alkhaldi

Department of Mathematics, College of Science, King Khalid University, P. O. Box 9004, Abha, Saudi Arabia

E-mail Address: ahalkhaldi@kku.edu.sa

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, and

Pradip Mandal

Department of Mathematics, The University of Burdwan, Golapbag, Burdwan 713104, West Bengal, India

E-mail Address: pradip2621994@rediffmail.com

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https://doi.org/10.1142/S0219887818501499Cited by:10 (Source: Crossref)

Abstract

This paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide an example of such submanifolds and obtain many new results including the necessary and sufficient conditions under which the submanifolds are totally geodesic. The Ricci solitons of such submanifolds are also studied.

Keywords:

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