The eigenvalues of β-Laplacian of slant submanifolds in complex space forms

Abstract

In this paper, we provided various estimates of the first nonzero eigenvalue of the $ \beta $-Laplacian operator on closed orientated $ p $-dimensional slant submanifolds of a $ 2m $-dimensional complex space form $ \widetilde{\mathbb{V}}^{2m}(4\epsilon) $ with constant holomorphic sectional curvature $ 4\epsilon $. As applications of our results, we generalized the Reilly-inequality for the Laplacian to the $ \beta $-Laplacian on slant submanifolds of a complex Euclidean space and a complex projective space.

Keywords

• eigenvalues
• elliptical laplacian operators
• complex space forms
• slant submanifolds
• $ \beta $-laplcians operators