Second Eigenvalue of a Jacobi Operator of Hypersurfaces with Constant Scalar Curvature
نویسندگان
چکیده
Let x : M → Sn+1(1) be an n-dimensional compact hypersurface with constant scalar curvature n(n − 1)r, r ≥ 1, in a unit sphere Sn+1(1), n ≥ 5, and let Js be the Jacobi operator of M . In 2004, L. J. Aĺıas, A. Brasil and L. A. M. Sousa studied the first eigenvalue of Js of the hypersurface with constant scalar curvature n(n− 1) in Sn+1(1), n ≥ 3. In 2008, Q.-M. Cheng studied the first eigenvalue of the Jacobi operator Js of the hypersurface with constant scalar curvature n(n−1)r, r > 1, in Sn+1(1). In this paper, we study the second eigenvalue of the Jacobi operator Js of M and give an optimal upper bound for the second eigenvalue of Js.
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