Abstract
This study attempts to establish new upper bounds on the mean curvature and constant sectional curvature of the first positive eigenvalue of the
ψ
− Laplacian operator on Riemannian manifolds. Various approaches are being used to find the first eigenvalue for the
ψ
− Laplacian operator on closed oriented bi-slant submanifolds in a Sasakian space form. We extend different Reilly-like inequalities to the
ψ
− Laplacian on bi-slant submanifolds in a unit sphere depending on our results for the Laplacian operator. The conclusion of this study considers some special cases as well.