Hypersurfaces with constant mean curvature and two principal curvatures in n+1

Hypersurfaces with constant mean curvature and two principal curvatures in n+1

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In this paper we consider compact oriented hypersurfaces M with constant mean curvature and two principal curvatures immersed in the Euclidean sphere.In the minimal case, Perdomo (Perdomo 7BP@Pk 2004) andWang (Wang 2003) obtained an integral inequality involving the square of the norm of the second fundamental form of M, where equality holds only if M is the Clifford POT torus.In this paper, using the traceless second fundamental form of M, we extend the above integral formula to hypersurfaces with constant mean curvature and give a new characterization of the H(r)-torus.