对偶平坦(α,β)-度量的共形不变性

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英文篇名：The Conformal Invariances of the Dually Flat(α,β)-metrics 作者：程新跃 ; 黄勤荣 ; 吴莎莎 英文作者：Xin Yue CHENG;Qin Rong HUANG;Sha Sha WU;School of Mathematical Sciences, Chongqing Normal University;School of Sciences, Chongqing University of Technology; 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 英文关键词：conformal transformation;;locally dually flat Finsler metric;;(α,β)-metric;;general Kropina metric 中文刊名：SXXB 英文刊名：Acta Mathematica Sinica(Chinese Series) 机构：重庆师范大学数学科学学院;重庆理工大学理学院; 出版日期：2019-05-15 出版单位：数学学报(中文版) 年：2019 期：v.62 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) 语种：中文; 页：SXXB201903006 页数：12 CN：03 ISSN：11-2038/O1 分类号：47-58

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.

引文

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