Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applications

Authors

  • Shunzi Guo School of Mathematics of Sichuan University Chengdu, 610065, People’s Republic of China, School of Mathematics and Statistics of Minnan Normal University, Zhangzhou 363000, People’s Republic of China

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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Articles

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