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);
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.
|Uncontrolled Keywords:||lightlike principal curvature
directions, lightlike asymptotic directions, lightlike umbilics|
|Subjects:||53-xx DIFFERENTIAL GEOMETRY|