THE CENTER MAP OF AN AFFINE IMMERSION

FURUHATA, Hitoshi; VRANCKEN, Luc

Hokkaido University Preprint Series in Mathematics, 2004, 665, 1-22

Permalink : https://doi.org/10.14943/83816

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DOI	https://doi.org/10.14943/83816
URI	https://hdl.handle.net/2115/69470
タイトル	THE CENTER MAP OF AN AFFINE IMMERSION
著者	著者名 FURUHATA, Hitoshi
著者	著者名 VRANCKEN, Luc
言語	英語
キーワード	affine sphere
	Tchebychev operator
	projectively flat affine surface
発行日	2004
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	665
ページ	1-22
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record