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

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˜2k+1(ϵ), with a constant ψ1-sectional curvature, ϵ. From our main results, we recovered the Reilly-type inequalities, which were proven before this study.