Czechoslovak Mathematical Journal, Vol. 70, No. 3, pp. 881-890, 2020


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

Jiancheng Liu, Rong Mi

Received December 28, 2018.   Published online February 24, 2020.

Abstract:  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.
Keywords:  Jacobi operator; first eigenvalue; closed hypersurface
Classification MSC:  53C50
DOI:  10.21136/CMJ.2020.0579-18

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Affiliations:   Jiancheng Liu, Rong Mi (corresponding author), College of Mathematics and Statistics, Northwest Normal University, 967 Anning E Rd, Anning, Lanzhou 730070, Gansu, P. R. China, e-mail: liujc@nwnu.edu.cn, mr8231227@163.com


 
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