New estimates for the first eigenvalue of the Jacobi operator on closed hypersurfaces in Riemannian space forms

Liu, Jiancheng ; Mi, Rong

Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 881-890

Abstract (VO)

We study the first eigenvalue of the Jacobi operator on closed hypersurfaces with constant mean curvature in non-flat Riemannian space forms. Under an appropriate constraint on the totally umbilical tensor of the hypersurfaces and following Meléndez's ideas in J. Meléndez (2014) we obtain a new sharp upper bound of the first eigenvalue of the Jacobi operator.

Détail

DOI : 10.21136/CMJ.2020.0579-18

Classification : 53C50
Keywords: Jacobi operator; first eigenvalue; closed hypersurface

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