Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applications
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 su...
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| Format: | Article |
| Language: | English |
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Republic of Armenia National Academy of Sciences
2015-05-01
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| Series: | Armenian Journal of Mathematics |
| Online Access: | http://armjmath.sci.am/index.php/ajm/article/view/108 |
| Summary: | 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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| ISSN: | 1829-1163 |