Abstract

The paper generalizes the self-adjoint differentialoperatoron hypersurfaces of a constant curvature manifoldto submanifolds, introduced by Cheng-Yau. Using the series ofsuch operators, a new way to prove Minkowski-Hsiung integralformula is given and some integral formulas for compact subman-ifolds is derived. An application to a hypersurface of a Rieman-nian manifold with harmonic Riemannian curvature is presented.

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