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A generalization of Lelieuvre’s formula to equiaffine immersions of general codimension

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Abstract

A non-degenerate equiaffine immersion of codimension one into an equiaffine space is locally expressed in terms of its conormal map and its affine fundamental form. The expression is called the Lelieuvre’s formula. We recently defined the notions of an equiaffine immersion of general codimension and its transversal volume element map. In this paper, we locally express a non-degenerate equiaffine immersion of general codimension into an equiaffine space in terms of its transversal volume element map and its affine fundamental form.

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  1. Department of Mathematics, Faculty of Science, Science University of Tokyo, Wakamiya-cho 26, Shinjuku-ku Tokyo, 162-8601, Japan

    Naoyuki Koike

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  1. Naoyuki Koike
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Correspondence to Naoyuki Koike.

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Koike, N. A generalization of Lelieuvre’s formula to equiaffine immersions of general codimension. Results. Math. 43, 150–155 (2003). https://doi.org/10.1007/BF03322730

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  • DOI: https://doi.org/10.1007/BF03322730

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