Operator ^r on a submanifold of Riemannian manifold and its applications - Guo, Shunzi (Armenian Journal of Mathematics, 2015)
The paper generalizes the self-adjoint differential operator on hypersurfaces of a constant curvature manifold to submanifolds, introduced by Cheng-Yau. Using the series of such operators, a new way to prove Minkowski-Hsiung integral formula is given and some integral formulas for compact submanifolds is derived. An application to a hypersurface of a Riemannian manifold with harmonic Riemannian curvature is presented.