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Hokkaido University Preprint Series in Mathematics >
THE CENTER MAP OF AN AFFINE IMMERSION
| Title: | THE CENTER MAP OF AN AFFINE IMMERSION |
| Authors: | FURUHATA, Hitoshi Browse this author | | VRANCKEN, Luc Browse this author |
| Keywords: | affine sphere | | Tchebychev operator | | projectively flat affine surface |
| Issue Date: | 2004 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 665 |
| Start Page: | 1 |
| End Page: | 22 |
| Abstract: | We study the center map of an equiaffine immersion which is introduced using the equiaffine support function. The center map is a constant map if and only if the hypersurface is an equiaffine sphere. We investigate those immersions for which the center map is affine congruent with the original hypersurface. In terms of centroaffine geometry, we show that such hypersurfaces provide examples of hypersurfaces with vanishing centroaffine Tchebychev operator. We also characterize them in equiaffine differential geometry using a curvature condition involving the covariant derivative of the shape operator. From both approaches, assuming the dimension is 2 and the surface is definite, a complete classification follows. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69470 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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