pick invariant
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scholarly journals Affine spheres with prescribed Blaschke metric

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5967-5975
Author(s):  
Barbara Opozda
Keyword(s):  
Gaussian Curvature ◽  
Harmonic Functions ◽  
Necessary Condition ◽  
Dimensional Manifold ◽  
Affine Sphere ◽  
Metric Tensor ◽  
Affine Spheres ◽  
Pick Invariant ◽  
Sufficient And Necessary Condition

It is proved that the equality ?ln |k-?| = 6k, where k is the Gaussian curvature of a metric tensor 1 on a 2-dimensional manifold is a sufficient and necessary condition for local realizability of the metric as the Blaschke metric of some affine sphere. Consequently, the set of all improper local affine spheres with nowhere-vanishing Pick invariant can be parametrized by harmonic functions.

scholarly journals Affine semiparallel surfaces with constant Pick invariant

2005 ◽  
Vol 34 (2) ◽  
pp. 355-374 ◽  
Author(s):  
Mohamed BELKHELFA ◽  
Masao KATOU
Keyword(s):  
Pick Invariant

Affine homogeneous surfaces in ℝ3 with vanishing pick invariant

1997 ◽  
Vol 67 (1) ◽  
pp. 105-115 ◽  
Author(s):  
B. E. Abdalla ◽  
F. Dillen ◽  
L. Vrancken
Keyword(s):  
Pick Invariant

Pick invariant and affine Gauss-Kronecker curvature

1993 ◽  
Vol 45 (1) ◽  
pp. 41-47 ◽  
Author(s):  
F. Milán
Keyword(s):  
Pick Invariant

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 On the Pick invariant

1988 ◽  
Vol 38 (3) ◽  
pp. 493-497
Author(s):  
Alois Švec
Keyword(s):  
Pick Invariant
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