On the marginally trapped surfaces in 4-dimensional space-times with finite type Gauss map

2013 ◽  
Vol 46 (1) ◽  
Author(s):  
Nurettin Cenk Turgay
Keyword(s):  
Finite Type ◽  
Dimensional Space ◽  
Gauss Map ◽  
Trapped Surfaces ◽  
Marginally Trapped Surfaces

Ruled submanifolds with finite type Gauss map

1994 ◽  
Vol 49 (1-2) ◽  
pp. 42-45 ◽  
Author(s):  
Christos Baikoussis
Keyword(s):  
Finite Type ◽  
Gauss Map

scholarly journals Ruled Surfaces and Tubes with Finite Type Gauss Map

1993 ◽  
Vol 16 (2) ◽  
pp. 341-349 ◽  
Author(s):  
Christos BAIKOUSSIS ◽  
Bang-yen CHEN ◽  
Leopold VERSTRAELEN
Keyword(s):  
Finite Type ◽  
Gauss Map ◽  
Ruled Surfaces

scholarly journals Isothermic surfaces in sphere geometries as Moutard nets

2007 ◽  
Vol 463 (2088) ◽  
pp. 3171-3193 ◽  
Author(s):  
Alexander I Bobenko ◽  
Yuri B Suris
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauss Map ◽  
Point Property ◽  
Property A ◽  
Lie Geometry ◽  
Möbius Geometry ◽  
Isothermic Surfaces ◽  
Three Dimensional Space

We give an elaborated treatment of discrete isothermic surfaces and their analogues in different geometries (projective, Möbius, Laguerre and Lie). We find the core of the theory to be a novel characterization of discrete isothermic nets as Moutard nets. The latter are characterized by the existence of representatives in the space of homogeneous coordinates satisfying the discrete Moutard equation. Moutard nets admit also a projective geometric characterization as nets with planar faces with a five-point property: a vertex and its four diagonal neighbours span a three-dimensional space. Restricting the projective theory to quadrics, we obtain Moutard nets in sphere geometries. In particular, Moutard nets in Möbius geometry are shown to coincide with discrete isothermic nets. The five-point property, in this particular case, states that a vertex and its four diagonal neighbours lie on a common sphere, which is a novel characterization of discrete isothermic surfaces. Discrete Laguerre isothermic surfaces are defined through the corresponding five-plane property, which requires that a plane and its four diagonal neighbours share a common touching sphere. Equivalently, Laguerre isothermic surfaces are characterized by having an isothermic Gauss map. S-isothermic surfaces as an instance of Moutard nets in Lie geometry are also discussed.

Hyperbolic submanifolds with finite type hyperbolic Gauss map

2015 ◽  
Vol 26 (02) ◽  
pp. 1550014 ◽  
Author(s):  
Uğur Dursun ◽  
Rüya Yeğin
Keyword(s):  
Scalar Curvature ◽  
Finite Type ◽  
Hyperbolic Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Scalar Curvature ◽  
Gauss Map ◽  
Hyperbolic Spaces ◽  
Nonzero Constant ◽  
Hyperbolic Gauss Map

We study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss map. Then we prove that a non-totally umbilical hypersurface Mn with nonzero constant mean curvature in a hyperbolic space [Formula: see text] has 2-type hyperbolic Gauss map if and only if M has constant scalar curvature. We also classify surfaces with constant mean curvature in the hyperbolic space [Formula: see text] having 2-type hyperbolic Gauss map. Moreover we show that a horohypersphere in [Formula: see text] has biharmonic hyperbolic Gauss map.

scholarly journals New examples of marginally trapped surfaces and tubes in warped spacetimes

2010 ◽  
Vol 27 (14) ◽  
pp. 145021 ◽  
Author(s):  
J L Flores ◽  
S Haesen ◽  
M Ortega
Keyword(s):  
Trapped Surfaces ◽  
Marginally Trapped Surfaces

Looking for marginally trapped surfaces

1991 ◽  
Vol 8 (5) ◽  
pp. L115-L118 ◽  
Author(s):  
K P Tod
Keyword(s):  
Trapped Surfaces ◽  
Marginally Trapped Surfaces
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