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 |
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doaj-5676f2d53447439495567c8db3a090702020-11-25T00:38:33ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632015-05-0171Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applicationsShunzi Guo0School 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 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. http://armjmath.sci.am/index.php/ajm/article/view/108 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Shunzi Guo |
| spellingShingle |
Shunzi Guo Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applications Armenian Journal of Mathematics |
| author_facet |
Shunzi Guo |
| author_sort |
Shunzi Guo |
| title |
Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applications |
| title_short |
Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applications |
| title_full |
Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applications |
| title_fullStr |
Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applications |
| title_full_unstemmed |
Operator $\Box^{r}$ on a submanifold of Riemannian manifold and its applications |
| title_sort |
operator $\box^{r}$ on a submanifold of riemannian manifold and its applications |
| publisher |
Republic of Armenia National Academy of Sciences |
| series |
Armenian Journal of Mathematics |
| issn |
1829-1163 |
| publishDate |
2015-05-01 |
| description |
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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| url |
http://armjmath.sci.am/index.php/ajm/article/view/108 |
| work_keys_str_mv |
AT shunziguo operatorboxronasubmanifoldofriemannianmanifoldanditsapplications |
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1725296917764636672 |