Bounds for Eigenvalues of q -Laplacian on Contact Submanifolds of Sasakian Space Forms

Yanlin Li, Fatemah Mofarreh, Abimbola Abolarinwa, Norah Alshehri and Akram Ali ()
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Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Fatemah Mofarreh: Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia
Abimbola Abolarinwa: Department of Mathematics, University of Lagos, Akoka, Lagos 101017, Nigeria
Norah Alshehri: Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia
Akram Ali: Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia

Mathematics, 2023, vol. 11, issue 23, 1-14

Abstract: This study establishes new upper bounds for the mean curvature and constant sectional curvature on Riemannian manifolds for the first positive eigenvalue of the q -Laplacian. In particular, various estimates are provided for the first eigenvalue of the q -Laplace operator on closed orientated ( l + 1 ) -dimensional special contact slant submanifolds in a Sasakian space form, M ˜ 2 k + 1 ( ϵ ) , with a constant ψ 1 -sectional curvature, ϵ . From our main results, we recovered the Reilly-type inequalities, which were proven before this study.

Keywords: slant submanifolds; Reilly-type inequality; q-Laplacian; eigenvalue estimates; Sasakian space form (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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