scholarly journals Umbilical Spacelike Submanifolds of Arbitrary Co-dimension

2017 ◽  
pp. 41-50
Author(s):  
Nastassja Cipriani ◽  
José M. M. Senovilla
Keyword(s):  
Spacelike Submanifolds

Spacelike submanifolds of codimension two in anti-de Sitter space

2017 ◽  
Vol 98 (6) ◽  
pp. 1165-1180
Author(s):  
Donghe Pei ◽  
Yongqiao Wang
Keyword(s):  
De Sitter Space ◽  
De Sitter ◽  
Codimension Two ◽  
Spacelike Submanifolds

scholarly journals The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space

2007 ◽  
Vol 13 (1) ◽  
pp. 23-55 ◽  
Author(s):  
Shyuichi Izumiya ◽  
María del Carmen Romero Fuster
Keyword(s):  
Minkowski Space ◽  
Codimension Two ◽  
Spacelike Submanifolds ◽  
Flat Geometry

Trapped submanifolds contained into a null hypersurface of de Sitter spacetime

2018 ◽  
Vol 20 (08) ◽  
pp. 1750059 ◽  
Author(s):  
Luis J. Alías ◽  
Verónica L. Cánovas ◽  
Marco Rigoli
Keyword(s):  
Steady State ◽  
State Space ◽  
Light Cone ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Round Sphere ◽  
Codimension Two ◽  
The Past ◽  
Sitter Spacetime ◽  
Spacelike Submanifolds

We study codimension two trapped submanifolds contained into one of the two following null hypersurfaces of de Sitter spacetime: (i) the future component of the light cone, and (ii) the past infinite of the steady state space. For codimension two compact spacelike submanifolds in the light cone we show that they are conformally diffeomorphic to the round sphere. This fact enables us to deduce that the problem of characterizing compact marginally trapped submanifolds into the light cone is equivalent to solving the Yamabe problem on the round sphere, allowing us to obtain our main classification result for such submanifolds. We also fully describe the codimension two compact marginally trapped submanifolds contained into the past infinite of the steady state space and characterize those having parallel mean curvature field. Finally, we consider the more general case of codimension two complete, non-compact, weakly trapped spacelike submanifolds contained into the light cone.

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