Dept. Math, Hokkaido Univ. EPrints Server

Global properties on spacelike submanifolds of codimension two in Minkowski space

Preprint Series # 878
Izumiya, Shyuichi and Nuno Ballesteros, Juan Jose and Romero Fuster, Maria del Carmen Global properties on spacelike submanifolds of codimension two in Minkowski space. (2007);

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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.

Item Type:Preprint
Additional Information:40
Uncontrolled Keywords:lightlike principal curvature directions, lightlike asymptotic directions, lightlike umbilics
Subjects:53-xx DIFFERENTIAL GEOMETRY
ID Code:1776