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 |
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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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