Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applications
Abstract
The paper generalizes the self-adjoint differential operator $\Box$ 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.
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Published
2015-05-27
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How to Cite
Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applications. (2015). Armenian Journal of Mathematics, 7(1), 6-31. https://armjmath.sci.am/index.php/ajm/article/view/108