Characterizations of a Clifford hypersurface in a unit sphere via Simons' integral inequalities

초록

Let M be an n(>= 3)-dimensional closed hypersurface in a unit sphere with constant m-th order mean curvature and with two distinct principal curvatures. We obtain a sharp curvature integral for M in terms of Ricci curvature, which gives a characterization of a Clifford hypersurface. Moreover we give a generalization of Simons' integral inequality for closed hypersurface with vanishing m-th order mean curvature by making use of the Laplacian of the function of principal curvatures.

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