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manuscripta mathematica

, Volume 96, Issue 4, pp 517–534 | Cite as

Moebius geometry of submanifolds in ? n

  • Changping Wang

Abstract:

In this paper we define a Moebius invariant metric and a Moebius invariant second fundamental form for submanifolds in ? n and show that in case of a hypersurface with n≥ 4 they determine the hypersurface up to Moebius transformations. Using these Moebius invariants we calculate the first variation of the moebius volume functional. We show that any minimal surface in ? n is also Moebius minimal and that the image in ? n of any minimal surface in ℝ n unter the inverse of a stereographic projection is also Moebius minimal. Finally we use the relations between Moebius invariants to classify all surfaces in ?3 with vanishing Moebius form.

Mathematics Subject Classification (1991):53A30, 53B25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Changping Wang
    • 1
  1. 1.Department of Mathematics, Peking University, Beijing 100871, People's Republic of China. e-mail: wangcp@pku.edu.cnCN

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