度量空间中拟双曲距离与对数距离的几何特征

沙沙 严(贵州师范大学数学科学学院，中国)

摘要

根据拟双曲距离和对数距离的基本概念及性质，刻画拟双曲距离和对数距离在度量空间中的一些几何性质。利用拟双曲度量作为研究的重要工具，再结合测地线和拟双曲测地线的概念与拟双曲距离和对数距离之间的关系，得到了对数距离测地线的一个等价条件和在拟双曲测地线的条件下，拟双曲开球与相关的度量开球之间的一个包含关系。研究结果表明：假设XDX⊆, , ,xyz D∈I()(),DDxz≤δδ()()(),, ,DD Djxz jxy jyz= +I()()().DD Dxyzδδ δ<≤()0, , ,kM y B xM> ∈∂N.[],,kz J xy∈>()(), 1 ,,kB z z y u B xM− +⊆

关键词

拟双曲度量；对数距离；测地线；度量空间

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DOI: http://dx.doi.org/10.12345/jxffcxysj.v7i13.21886