摘要
首先证明对开集GRn,广义双曲度量jGp是Gromov双曲的当且仅当G只有一个边界点,这是文献[5]中Hast的结果的推广;然后借助证明Apollon度量的Gromov双曲性得到对于任意的区域GRn(Card G≥2),广义双曲度量δpG是Gromov双曲的;最后证明对区域GRn(n≥3),关于广义双曲度量jpG和δpG的等距变换是Mbius变换,对于后者G应满足CardG≥2.
For any open set G belong to R^n, it is shown that the generalized hyperbolic metric jG^p is Gromov hyperbolic if and only if G has only one boundary point. This is the generalization of the result of Haisto in [ 5 ]. By proving the Gromov hyperbolicity of the Apollonian metric, it is shown that for any domain G belong to R^n（ Card 偏d G≥2） , the generalized hyperbolic metric is Gromov hyperbolic. For any domain G belong to R^n（n≥3 ） with Card 偏d 9G≥2, it is proven that isometries between the generalized hyperbolic metrics and are M？ bius transformations.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2007年第4期498-502,507,共6页
Journal of Natural Science of Heilongjiang University
