6533b862fe1ef96bd12c6284

RESEARCH PRODUCT

Global properties of codimension two spacelike submanifolds in Minkowski space

Maria Del Carmen Romero FusterJuan José Nuño BallesterosShyuichi Izumiya

subject

Pure mathematicseducationMinkowski's theoremMathematical analysisNormal curvatureOrder (ring theory)CodimensionNormal fieldGlobal informationGeneral Relativity and Quantum CosmologyHyperplaneMinkowski spaceMathematics::Differential GeometryGeometry and TopologyMathematics

description

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.

yearjournalcountryeditionlanguage
2009-09-10advg
https://doi.org/10.1515/advgeom.2009.034