A Moebius characterization of Veronese surfaces in
$S^n$ |
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| Authors: | Haizhong Li Changping Wang Faen Wu |
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| Institution: | (1) Department of Mathematical Sciences, Tsinghua Unviersity, Beijing 100084, People's Republic of China (e-mail: hli@math.tsinghua.edu.cn) , CN;(2) Department of Mathematics, Peking University, Beijing 1000871, People's Republic of China (e-mail: wangcp@pku.edu.cn) , CN;(3) Department of Mathematics, Northern Jiaotong University, Beijing, 100044, People's Republic of China (e-mail: fewu@center.njtu.edu.cn) , CN |
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| Abstract: | Let be an umbilic-free submanifold in with I and II as the first and second fundamental forms. An important Moebius invariant for in Moebius differential geometry is the so-called Moebius form , defined by , where is a local basis of the tangent bundle with dual basis , is a local basis of the normal bundle, is the mean curvature vector and . In this paper we prove that if is an umbilics-free immersion of 2-sphere with vanishing Moebius form , then there exists a Moebius transformation and a 2k-equator with such that is the Veronese surface.
Received August 12, 1999 / Published online March 12, 2001 |
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| Keywords: | Mathematics Subject Classification (2000): 53A30 53C42 53A10 |
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