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# Global properties on spacelike submanifolds of codimension two in Minkowski space

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 Title: Global properties on spacelike submanifolds of codimension two in Minkowski space Authors: Izumiya, Shyuichi Browse this author Nuno Ballesteros, Juan Jose Browse this author Romero Fuster, Maria del Carmen Browse this author Keywords: lightlike principal curvature directions lightlike asymptotic directions lightlike umbilics Issue Date: 10-Oct-2007 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 878 Start Page: 1 End Page: 25 Abstract: We consider codimension two spacelike submanifolds with a parallel normal field (i.e. vanishing normal curvature) in Minkowski space. We use the analysis of their contacts with hyperplane and hyperquadrics in order to get some global informations on them. As a consequence we obtain new versions of Carat¥`eodory's and Loewner's conjectures on spacelike surfaces in $4$-dimensional Minkowski space and $4$-flattenings therorems for closed spacelike curves in $3$-dimensional Minkowski space. Type: bulletin (article) URI: http://hdl.handle.net/2115/69687 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics