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

Izumiya, Shyuichi; Romero Fuster, Maria del Carmen

Selecta Mathematica, New Series, 2007, 13(1), 23-55

Permalink : https://hdl.handle.net/2115/28202

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アクセス権	open access
URI	https://hdl.handle.net/2115/28202
タイトル	The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space
著者	e-Rad_Researcher 80127422 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	2007-03
出版者	Birkhäuser Basel (Springer Science+Business Media)
収録物名	Selecta Mathematica, New Series
巻(号)	13(1)
ページ	23-55
抄録	We introduce the notion of the lightcone Gauss–Kronecker curvature for a spacelike submanifold of codimension 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	学術雑誌論文
出版タイプ	Accepted Manuscript
PISSN	1022-1824
EISSN	1420-9020
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.1007/s00029-007-0033-9