A Moebius characterization of Veronese surfaces in S-n | |
Li, HZ ; Wang, CP ; Wu, F | |
2001 | |
英文摘要 | Let M-m be an umbilic-fret submanifold in S-n with I and II as the first and second fundamental forms. An important Moebius invariant for M-m in Moebius differential geometry is the so-called Moebius form Phi .defined by Phi = -rho (-2) Sigma (i,alpha) (H-i(alpha) + Sigma (j)(IIijalpha - (HIij)-I-alpha)e(j)(log rho))omega (i) circle times e(alpha), where (e(i)) is it local basis of the tangent bundle with dual basis (omega (i)), (e(alpha)) is a local basis of the normal bundle, H = Sigma (alpha) H(alpha)e(alpha) is the mean curvature vector and rho = rootm/m-1 parallel to II - HI parallel to. In this paper we prove that if x : S-2 --> S-n is an umbilics-free immersion of 2-sphere with vanishing Moebius form Phi. then there exists a Moebius transformation tau : S-n --> S-n and a 2k-equator S-2k subset of S-n with 2 less than or equal to k less than or equal to [n/2] such that tau o x S-2 --> S-2k is the Veronese surface.; Mathematics; SCI(E); 26; ARTICLE; 4; 707-714; 319 |
语种 | 英语 |
出处 | SCI |
出版者 | mathematische annalen |
内容类型 | 其他 |
源URL | [http://hdl.handle.net/20.500.11897/211211] ![]() |
专题 | 数学科学学院 |
推荐引用方式 GB/T 7714 | Li, HZ,Wang, CP,Wu, F. A Moebius characterization of Veronese surfaces in S-n. 2001-01-01. |
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