对偶平坦(α,β)-度量的共形不变性  

The Conformal Invariances of the Dually Flat(α,β)-metrics

作　　者：程新跃 黄勤荣 吴莎莎 Xin Yue CHENG;Qin Rong HUANG;Sha Sha WU(School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China;School of Sciences, Chongqing University of Technology, Chongqing 400054, P. R. China)

机构地区：[1]重庆师范大学数学科学学院 [2]重庆理工大学理学院

出　　处：《数学学报（中文版）》2019年第3期397-408,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11871126;11371386);重庆师范大学科学基金(17XLB022)

摘　　要：本文主要研究了两个(α,β)-度量之间的共形变换.证明了:若F是一个局部对偶平坦的正则(α,β)-度量且与度量■共形相关,即■,那么度量■也是一个局部对偶平坦的(α,β)-度量当且仅当共形变换是一个位似.进一步,在度量具有奇异性的情形,我们证明了两个局部对偶平坦广义Kropina度量之间的任一共形变换必然是一个位似.We study the conformal transformations between two(α,β)-metrics. We prove that, if F is a locally dually flat regular(α,β)-metric and is conformally related to ■, that is,■, then ■ is also a locally dually flat(α,β)-metric if and only if the conformal transformation is a homothety. Further, in the case with singularity,we prove that any conformal transformation between two locally dually flat general Kropina metrics must be a homothety.

关 键 词：共形变换 局部对偶平坦芬斯勒度量 (Α Β)-度量 广义Kropina度量 

分 类 号：O186.14[理学—数学]