Journal
AIMS MATHEMATICS
Volume 7, Issue 9, Pages 16054-16066Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2022879
Keywords
eigenvalues; Laplacian; pseudo-slant submanifolds; generalized Sasakian space form
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The study aims 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. Various methods are used to determine the first eigenvalue for the alpha-Laplacian operator on closed oriented pseudo-slant submanifolds in a generalized Sasakian space form.
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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