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Submanifolds with finite type Gauss map

Published online by Cambridge University Press:  17 April 2009

Bang-yen Chen  and
Paolo Piccinni
Bang-yen Chen
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, U.S.A.
Paolo Piccinni
Affiliation:
Dipartimento di Matematica, Università di Roma “La Sapienza”, 00185 Rome, Italy
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Abstract

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In this paper we study the following problem: To what extent does the type of the Gauss map of a submanifold of Em determine the submanifold? Several results in this respect are obtained. In particular, submanifolds with 1-type Gauss map are characterized. Surfaces with 1-type Gauss map and minimal surfaces of Sm−1 with 2-type Gauss map are completely classified. Some applications are also given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 2 , April 1987 , pp. 161 - 186
Copyright
Copyright © Australian Mathematical Society 1987

References

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