Armenian Journal of Mathematics

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

Guo, Shunzi (2015) Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applications. Armenian Journal of Mathematics, 7 (1). pp. 6-31. ISSN 1829-1163

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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.

Item Type:Article
Uncontrolled Keywords:Newton tensor, operator, submanifold, hypersurface, Codazzi tensor
Subjects:14-xx Algebraic geometry
20-xx Group theory and generalizations
46-xx Functional analysis
53-xx Differential geometry
ID Code:444
Deposited By:guoshunzi Shunzi Guo
Deposited On:27 May 2015 00:39
Last Modified:27 May 2015 00:39

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