The Gauss map of a spacelike constant mean curvature hypersurface of Minkowski space

1990 ◽  
Vol 65 (1) ◽  
pp. 52-57 ◽  
Author(s):  
Bennett Palmer
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gauss Map ◽  
Constant Mean Curvature Hypersurface ◽  
Curvature Hypersurface

Symmetry-Breaking for Immersed Constant Mean Curvature Hypersurfaces

2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Mohamed Jleli
Keyword(s):  
Symmetry Breaking ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Jacobi Operator ◽  
Constant Mean Curvature Hypersurfaces ◽  
The Family ◽  
Constant Mean Curvature Hypersurface ◽  
Curvature Hypersurface

AbstractIn this paper we prove the existence of constant mean curvature hypersurfaces which are cylindrically bounded and which bifurcate from the family of immersed constant mean curvature hypersurface of revolution. Based on the study of the spectrum of the Jacobi operator (the linearized mean curvature) about this family, the existence of new branches follows from a bifurcation result of Crandall and Rabinowitz.

SOME CLASSIFICATIONS OF LORENTZIAN SURFACES WITH FINITE TYPE GAUSS MAP IN THE MINKOWSKI 4-SPACE

2015 ◽  
Vol 99 (3) ◽  
pp. 415-427 ◽  
Author(s):  
NURETTIN CENK TURGAY
Keyword(s):  
Minkowski Space ◽  
Finite Type ◽  
Minimal Surfaces ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gauss Map ◽  
Complete Classification ◽  
Nonzero Constant ◽  
Dimensional Minkowski Space

In this paper we study the Lorentzian surfaces with finite type Gauss map in the four-dimensional Minkowski space. First, we obtain the complete classification of minimal surfaces with pointwise 1-type Gauss map. Then, we get a classification of Lorentzian surfaces with nonzero constant mean curvature and of finite type Gauss map. We also give some explicit examples.

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