Equiaffine immersions of general codimension and its transversal volume element map |
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| Authors: | Naoyuki Koike Kouji Takekuma |
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| Institution: | 1. Department of Mathematics, Faculty of Science, Science University of Tokyo, Wakamiya-cho 26, Shinjuku-ku, Tokyo, 162, Japan
2. Department of Mathematics, Faculty of Science and Engineering, Chuo University, Kasuga 1-13-27, Bunkyo-ku, Tokyo, 112, Japan
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| Abstract: | With an equiaffine immersion of codimension 1 into the affine space with the natural equiaffine structure, the conormal map is associated. In this paper, for an equiaffine immersion of general codimension into the space, we shall define the map corresponding to the conormal map, which is called the transversal volume element map. And we shall investigate if, an equiaffine immersion of general codimension into the space is determined by its affine fundamental form and its transversal volume element map. |
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