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: 2002
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://hdl.handle.net/11536/29178
http://dx.doi.org/10.1090/S0002-9939-01-06030-0
ISSN: 0002-9939
DOI: 10.1090/S0002-9939-01-06030-0
期刊: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume: 130
Issue: 1
起始頁: 157
結束頁: 161
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