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 2004) andWang (Wang 2003) obtained an integral inequality involving the square cystorelin 100ml of the norm of the second fundamental form of M, where equality holds only if M is the Clifford torus.In this paper, using the traceless second fundamental form of M, we extend the above integral taylor made p790 for sale formula to hypersurfaces with constant mean curvature and give a new characterization of the H(r)-torus.