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

页码：160 / 175

页数：16

共 50 条

[41] Some projectively Ricci-flat (α, β)-metrics [J].

Gabrani, Mehran ;

Sevim, Esra Sengelen ;

Shen, Zhongmin .

PERIODICA MATHEMATICA HUNGARICA, 2023, 86 (02) :514-529

[42] On the Characterization of Conformally Flat Weakly Einstein Finsler Metrics [J].

Jangir, Seema ;

Shanker, Gauree .

KYUNGPOOK MATHEMATICAL JOURNAL, 2023, 63 (04) :611-622

[43] On Locally Projectively Flat Finsler Space of a Special Exponential Metric with Constant Flag Curvature [J].

Tripathi, B. K. ;

Khan, S. .

ARMENIAN JOURNAL OF MATHEMATICS, 2024, 16 (15) :1-11

[44] On a class of Ricci-flat Finsler metrics in Finsler geometry [J].

Chen, Bin ;

Shen, Zhongmin ;

Zhao, Lili .

JOURNAL OF GEOMETRY AND PHYSICS, 2013, 70 :30-38

[45] AN IMPORTANT CLASS OF CONFORMALLY FLAT WEAK EINSTEIN FINSLER METRICS [J].

Chen, Guangzu ;

Cheng, Xinyue .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2013, 24 (01)

[46] A class of Ricci-flat Finsler metrics [J].

Ulgen, Semail ;

Sevim, Esra S. .

ANNALES POLONICI MATHEMATICI, 2018, 121 (01) :73-83

[47] On a Class of Finsler Metrics of Scalar Flag Curvature [J].

Xia, Qiaoling .

RESULTS IN MATHEMATICS, 2017, 71 (1-2) :483-507

[48] RIGIDITY THEOREMS OF SOME DUALLY FLAT FINSLER METRICS AND ITS APPLICATIONS [J].

Shen, Bin ;

Tian, Yanfang .

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2016, 53 (05) :1457-1469

[49] On a class of locally dually flat Finsler metrics of isotropic flag curvature [J].

Xia, Qiaoling .

PUBLICATIONES MATHEMATICAE-DEBRECEN, 2011, 78 (01) :169-190

[50] On a new class of Finsler metrics [J].

Yu, Changtao ;

Zhu, Hongmei .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2011, 29 (02) :244-254

← 1 2 3 4 5 →