TY - JOUR
T1 - Rigidity of time-flat surfaces in the Minkowski spacetime
AU - Chen, Po Ning
AU - Wang, Mu Tao
AU - Wang, Ye Kai
N1 - Publisher Copyright:
© 2014 International Press.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2014
Y1 - 2014
N2 - A time-flat condition on spacelike 2-surfaces in spacetime is considered here. This condition is analogous to the constant torsion condition for curves in a three-dimensional space and has been studied in [2, 5, 6, 13, 14]. In particular, any 2-surface in a static slice of a static spacetime is time-flat. In this paper, we address the question in the title and prove several local and global rigidity theorems for such surfaces in the Minkowski and Schwarzschild spacetimes. Higher-dimensional generalizations are also considered.
AB - A time-flat condition on spacelike 2-surfaces in spacetime is considered here. This condition is analogous to the constant torsion condition for curves in a three-dimensional space and has been studied in [2, 5, 6, 13, 14]. In particular, any 2-surface in a static slice of a static spacetime is time-flat. In this paper, we address the question in the title and prove several local and global rigidity theorems for such surfaces in the Minkowski and Schwarzschild spacetimes. Higher-dimensional generalizations are also considered.
UR - http://www.scopus.com/inward/record.url?scp=84926432429&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84926432429&partnerID=8YFLogxK
U2 - 10.4310/MRL.2014.v21.n6.a1
DO - 10.4310/MRL.2014.v21.n6.a1
M3 - Article
AN - SCOPUS:84926432429
VL - 21
SP - 1227
EP - 1240
JO - Mathematical Research Letters
JF - Mathematical Research Letters
SN - 1073-2780
IS - 6
ER -