Acta mathematica scientia, Series B >
THE ASSOCIATED FAMILIES OF SEMI-HOMOGENEOUS COMPLETE HYPERBOLIC AFFINE SPHERES
Received date: 2015-03-31
Revised date: 2015-05-12
Online published: 2016-06-25
Supported by
The authors were supported by the NSF of China (10941002, 11001262), and the Starting Fund for Distinguished Young Scholars of Wuhan Institute of Physics and Mathematics (O9S6031001).
Hildebrand classified all semi-homogeneous cones in R3 and computed their cor-responding complete hyperbolic affine spheres. We compute isothermal parametrizations for Hildebrand's new examples. After giving their affine metrics and affine cubic forms, we con-struct the whole associated family for each of Hildebrand's examples. The generic member of these affine spheres is given by Weierstrass P, ζ and σ functions. In general any regular convex cone in R3 has a natural associated S1-family of such cones, which deserves further studies.
Zhicheng LIN , Erxiao WANG . THE ASSOCIATED FAMILIES OF SEMI-HOMOGENEOUS COMPLETE HYPERBOLIC AFFINE SPHERES[J]. Acta mathematica scientia, Series B, 2016 , 36(3) : 765 -781 . DOI: 10.1016/S0252-9602(16)30038-8
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