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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 E m 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 S m −1 with 2 -type Gauss map are completely classified. Some applications are also given.
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Chen et al. (1987) studied this question.
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