On the Pick Invariant, the Affine mean Curvature and the Gauss Curvature of Affine Surfaces

1991 ◽  
Vol 20 (3-4) ◽  
pp. 622-642 ◽  
Author(s):  
Franki Dillen ◽  
Antonio Martinez ◽  
Francisco Milan ◽  
Florentino Garcia Santos ◽  
Luc Vrancken
Keyword(s):  
Mean Curvature ◽  
Gauss Curvature ◽  
Affine Mean Curvature ◽  
Pick Invariant

scholarly journals Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

2014 ◽  
Vol 12 (9) ◽  
Author(s):  
Rafael López ◽  
Esma Demir
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gauss Curvature ◽  
First Case ◽  
Helicoidal Surfaces ◽  
Constant Gauss Curvature

AbstractWe classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.

The Affine Mean Curvature Vector for Surfaces in R4

1994 ◽  
Vol 166 (1) ◽  
pp. 155-165 ◽  
Author(s):  
F. Dillen ◽  
G. Mys ◽  
L. Verstraelen ◽  
L. Vrancken
Keyword(s):  
Mean Curvature ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Affine Mean Curvature

Blaschke hypersurfaces with constant negative affine mean curvature

2014 ◽  
Vol 47 (3) ◽  
pp. 225-238 ◽  
Author(s):  
An-Min Li ◽  
Li Sheng ◽  
Udo Simon
Keyword(s):  
Mean Curvature ◽  
Affine Mean Curvature
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