Estimation of eigenvalues for the $ \alpha $-Laplace operator on pseudo-slant submanifolds of generalized Sasakian space forms

Abstract

<abstract><p>In this study, we seek to establish new upper bounds for the mean curvature and constant sectional curvature of the first positive eigenvalue of the $ \alpha $-Laplacian operator on Riemannian manifolds. More precisely, various methods are used to determine the first eigenvalue for the $ \alpha $-Laplacian operator on the closed oriented pseudo-slant submanifolds in a generalized Sasakian space form. From our findings for the Laplacian, we extend many Reilly-like inequalities to the $ \alpha $-Laplacian on pseudo slant submanifold in a unit sphere.</p></abstract>