Estimation of eigenvalues for the α " role="presentation"> α α \alpha -Laplace operator on pseudo-slant submanifolds of generalized Sasakian space forms

AIMS Mathematics

article

Meraj Ali Khan¹  Ali H. Alkhaldi²  Mohd. Aquib³ 

[1]Department of Mathematics, University of Tabuk

[2]Department of Mathematics, College of Science King Khalid University

[3]Department of Mathematics, Sri Venkateshwara College, University of Delhi

关键词: eigenvalues;    Laplacian;    pseudo-slant submanifolds;    generalized Sasakian space form;   

DOI  :  10.3934/math.2022879

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY