Reduction of certain projectively flat Finsler metrics

被引：1
作者：
Zheng, Daxiao [1 ]
机构：
[1] Anhui Normal Univ, Dept Math & Stat, Wuhu 241000, Anhui, Peoples R China
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2019年 / 65卷
关键词：
General; (alpha; beta)-metric; Locally projectively; Flag curvature; Deformation; (ALPHA;
D O I：
10.1016/j.difgeo.2019.03.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study a class of Finsler metric defined by a Riemannian metric, a 1-form and its norm. We show that every non-trivial locally projectively flat metrics in such a form can be reexpressed to a special one defined by locally projectively flat Riemannian metric, a closed conformal 1-form and its norm in dimension n >= 3. (C) 2019 Published by Elsevier B.V.
引用
收藏
页码：160 / 175
页数：16
相关论文
共 50 条
[11]   ON A CLASS OF SINGULAR PROJECTIVELY FLAT FINSLER METRICS WITH CONSTANT FLAG CURVATURE [J].
Yang, Guojun .
INTERNATIONAL JOURNAL OF MATHEMATICS, 2013, 24 (10)
[12]   A Class of Projectively Flat Finsler Metrics [J].
Weidong SONG ;
Jingyong ZHU .
JournalofMathematicalResearchwithApplications, 2013, 33 (06) :737-744
[13]   GEOMETRY OF LOCALLY PROJECTIVELY FLAT FINSLER SPACE WITH CERTAIN (α, β)-METRIC [J].
Abbaniramakrishnappa, Ajaykumar ;
Kumar, Pradeep .
JOURNAL OF APPLIED MATHEMATICS & INFORMATICS, 2023, 41 (01) :193-203
[14]   ON A CLASS OF LOCALLY PROJECTIVELY FLAT FINSLER METRICS [J].
Mo, X. H. ;
Zhu, H. M. .
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2017, 43 (03) :735-746
[15]   On a class of projectively flat Finsler metrics with weakly isotropic flag curvature [J].
Chen, Guangzu ;
Cheng, Xinyue ;
Yuan, Mingao .
PERIODICA MATHEMATICA HUNGARICA, 2013, 67 (02) :155-166
[16]   On a New Class of Projectively Flat Finsler Metrics [J].
Li, Ying ;
Song, Wei-Dong .
JOURNAL OF MATHEMATICAL STUDY, 2016, 49 (01) :57-63
[17]   On some projectively flat finsler metrics in terms of hypergeometric functions [J].
Mo, Xiaohuan .
ISRAEL JOURNAL OF MATHEMATICS, 2011, 184 (01) :59-78
[18]   On a Class of Two-Dimensional Projectively Flat Finsler Metrics with Constant Flag Curvature [J].
Yang, Guo Jun .
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2013, 29 (05) :959-974
[19]   On projectively flat Finsler spaces [J].
Binh, T. Q. ;
Kertesz, D. Cs. ;
Tamassy, L. .
ACTA MATHEMATICA HUNGARICA, 2013, 141 (04) :383-400
[20]   On a class of projectively flat (α, β)-metrics [J].
Cheng, Xinyue ;
Li, Ming .
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2007, 71 (1-2) :195-205
12345