Moebius geometry of submanifolds in ?
n |
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Authors: | Changping Wang |
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Institution: | (1) Department of Mathematics, Peking University, Beijing 100871, People's Republic of China. e-mail: wangcp@pku.edu.cn, CN |
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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.
Received: 18 November 1997 |
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Keywords: | Mathematics Subject Classification (1991):53A30 53B25 |
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