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

Meraj Ali Khan; Ali H. Alkhaldi; Mohd. Aquib; Meraj Ali Khan; Ali H. Alkhaldi; Mohd. Aquib

doi:10.3934/math.2022879

AIMS Mathematics

2022, Volume 7, Issue 9: 16054-16066. doi: 10.3934/math.2022879

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Research article

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

1.
Department of Mathematics, University of Tabuk, Tabuk, Kingdom of Saudi Arabia
2.
Department of Mathematics, College of Science King Khalid University, Saudi Arabia
3.
Department of Mathematics, Sri Venkateshwara College, University of Delhi, New Delhi 110021, India

Received: 14 November 2021 Revised: 13 May 2022 Accepted: 01 June 2022 Published: 30 June 2022
MSC : 58C40, 53C42, 35P15

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.
- eigenvalues,
- Laplacian,
- pseudo-slant submanifolds,
- generalized Sasakian space form
Citation: Meraj Ali Khan, Ali H. Alkhaldi, Mohd. Aquib. Estimation of eigenvalues for the $ \alpha $-Laplace operator on pseudo-slant submanifolds of generalized Sasakian space forms[J]. AIMS Mathematics, 2022, 7(9): 16054-16066. doi: 10.3934/math.2022879

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Abstract

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.

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