The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space

Izumiya, Shyuichi; Romero Fuster, Maria del Carmen

Hokkaido University Preprint Series in Mathematics, 2006, 777, 1-31

Permalink : https://doi.org/10.14943/83927

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DOI	https://doi.org/10.14943/83927
URI	https://hdl.handle.net/2115/69585
タイトル	The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space
著者	著者名 Izumiya, Shyuichi
著者	著者名 Romero Fuster, Maria del Carmen
言語	英語
キーワード	lightcone Gauss map
	lightlike Gauss-Kronecker curvature
	Gauss-Bonnet Theorem
発行日	2006-04-01
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	777
ページ	1-31
抄録	We introduce the notion of the lightcone Gauss-Kronecker curvature for a spacelike submanifold of codimention two in Minkowski space which is a generalization of the ordinary notion of Gauss curvature of hypersurfaces in Euclidean space. In the local sense, this curvature describes the contact of such submanifolds with lightlike hyperplanes. We study geometric properties of such curvatures and show a Gauss-Bonnet type theorem. As examples we have hypersurfaces in hyperbolic space, spacelike hypersurfaces in the lightcone and spacelike hypersurfaces in de Sitter space.
資源タイプ	紀要論文
出版タイプ	Version of Record