THE ASSOCIATED FAMILIES OF SEMI-HOMOGENEOUS COMPLETE HYPERBOLIC AFFINE SPHERES  

作　　者：林至诚 王二小 

机构地区：[1]Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences [2]Department of Mathematics,Hong Kong University of Science and Technology

出　　处：《Acta Mathematica Scientia》2016年第3期765-781,共17页数学物理学报（B辑英文版）

基　　金：supported by the NSF of China(10941002,11001262);the Starting Fund for Distinguished Young Scholars of Wuhan Institute of Physics and Mathematics(O9S6031001)

摘　　要：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 construct the whole associated family for each of Hildebrand＇s examples. The generic member of these affine spheres is given by Weierstrass f,ζ and a functions. In general any regular convex cone in R^3 has a natural associated S^1-family of such cones, which deserves further studies.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 construct the whole associated family for each of Hildebrand＇s examples. The generic member of these affine spheres is given by Weierstrass f,ζ and a functions. In general any regular convex cone in R^3 has a natural associated S^1-family of such cones, which deserves further studies.

关 键 词：hyperbolic affine spheres isothermal coordinates Weierstrass elliptic functions Monge-Ampere equation Tzitzeica equation 

分 类 号：O186.1[理学—数学]