Global properties of codimension two spacelike submanifolds in Minkowski space-Reference-Cited by-同舟云学术

Global properties of codimension two spacelike submanifolds in Minkowski space

Published:2009-09-10 Issue:1 Volume:10 Page:51-75
ISSN:1615-7168
Container-title:advg
language:en
Short-container-title:

Author:

Izumiya Shyuichi¹,Nuño Ballesteros Juan José²,Romero Fuster María del Carmen²

Affiliation:

1. Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan. Email:

2. Departament de Geometría i Topología, Universitat de València, 46100 Burjassot (València), Spain Email:

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.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom.2009.034/pdf

Reference32 articles.

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