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- 2016
局部对称空间中线性Weingarten超曲面
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Abstract:
研究了局部对称空间中具有有界平均曲率的线性 Weingarten 超曲面 M^{n}. 通过对 M^{n} 上的对称张量 Φ 的模长进行适当限制, 得到了该类超曲面要么是 全脐的, 要么等距于一个具有两个主曲率的超曲面, 且其中一个主曲率的重数为 1.
： The complete linear Weingarten hypersurfaces with bounded mean curvature in locally symmetric manifold are studied. By supposing a suitable restriction on the norm of Φ which is symmetric tensor in M^{n}, it is proved that such a hypersurface must be either totally umbilical or isometric to the hypersurface with two distinct principle curvatures, one of which is simple
| [1] | SY Cheng, ST Yau.Hypersurfaces with constant scalar curvature[J].Math. Ann., 1977, 225(3):195-204 |
| [2] | S Shu.Complete hypersurfaces with constant scalar curvature in a hyperbolic space[J].Balkan J. Geom. Appl., 2007, 12(2):107-115 |
| [3] | H Li, YJ Suh, G Wei.Linear Weingarten hypersurfaces in a unit sphere[J].Bull. Korean Math. Soc., 2009, 46(2):321-329 |
| [4] | S Shu.Linear Weingarten hypersurfaces in a real space form[J].Glasgow Math. J., 2010, 52(3):635-648 |
| [5] | C P Aquino, H F de Lima, M A L Vel\'{a}squez.Linear Weingarten hypersurfaces with bounded mean curvature in the hyperbolic space[J].Glasgow Math. J., 2015, 57(3):653-663 |
| [6] | X Chao, P Wang.Linear Weingarten hypersurfaces in locally symmetric manifolds[J].Balkan J.Geom. Appl., 2014, 19(2):50-59 |
| [7] | M Okumura.Hypersurfaces and a pinching problem on the second fundamental tensor[J].Amer. J. Math., 1974, 63(1):207-213 |
| [8] | R L\'{o}pez.Rotational linear Weingarten surfaces of hyperbolic type[J].Israel J. Math., 2008, 167(1):283-301 |
| [9] | A Barros, J Silva, P Sousa.Rotational linear Weingarten surfaces into the Euclidean sphere[J].Israel J. Math., 2012, 192(2):819-830 |
| [10] | C P Aquino, H F de Lima, M A L Vel\'{a}squez.A new characterization of complete linear Weingarten hypersurfaces in real space forms[J].Pacific J. Math., 2013, 261(1):33-43 |
| [11] | C P Aquino, H F de Lima, M A L Vel\'{a}squez.Generalized maximum principles and the characterization of linear Weingarten hypersurfaces in space forms[J].Michigan Math. J., 2014, 63(1):27-40 |
| [12] | C P Aquino, H F de Lima.On the geometry of linear Weingarten hypersurfaces in the hyperbolic space[J].Monatsh. Math., 2013, 171(3-4):259-268 |
