標題: | A global pinching theorem for surfaces with constant mean curvature in S-3 |
作者: | Hsu, YJ Wang, TH 應用數學系 Department of Applied Mathematics |
關鍵字: | mean curvature;sphere;totally umbilical |
公開日期: | 1-一月-2001 |
摘要: | Let M be a compact immersed surface in the unit sphere S-3 with constant mean curvature H. Denote by phi the linear map from T-p(M) into Tp(M), phi = A - H/2 I, where A is the linear map associated to the second fundamental form and I is the identity map. Let Phi denote the square of the length of phi. We prove that if parallel to Phi parallel to (L2) less than or equal to C, then M is either totally umbilical or an H(r)-torus, where C is a constant depending only on the mean curvature H. |
URI: | http://dx.doi.org/10.1090/S0002-9939-01-06030-0 http://hdl.handle.net/11536/144952 |
ISSN: | 0002-9939 |
DOI: | 10.1090/S0002-9939-01-06030-0 |
期刊: | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY |
Volume: | 130 |
起始頁: | 157 |
結束頁: | 161 |
顯示於類別: | 期刊論文 |