Global properties of codimension two spacelike submanifolds in Minkowski space

descriptionPublicationkeyboard_double_arrow_right Article 10 Sep 2009 Germany English Publisher:Walter de Gruyter GmbHJournal:advg, volume 10, pages 51-75 (issn: 1615-715X, eissn: 1615-7168,

Copyright policy )

Authors: Izumiya, Shyuichi; Ballesteros, Juan José Nuño; Fuster, María del Carmen Romero;

doi: 10.1515/advgeom.2009.034

Global properties of codimension two spacelike submanifolds in Minkowski space

- Summary
- Subjects
- Metrics

Abstract

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 hyperplanes and hyperquadrics in order to get some global information on them. As a consequence we obtain new versions of Carathéodory's and Loewner's conjectures on spacelike surfaces in 4-dimensional Minkowski space and 4-flattenings theorems for closed spacelike curves in 3-dimensional Minkowski space.

Country

Germany

Related Organizations

Keywords

lightlike principal curvature directions, lightlike umbilics, Global submanifolds, Non-Euclidean differential geometry, lightlike principal asymptotic directions, flattenings

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	6
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average