On a class of Ricci-flat Finsler metrics in Finsler geometry

被引：8

作者：

Chen, Bin ^{[1
]}

Shen, Zhongmin ^{[2
]}

Zhao, Lili ^{[3
]}

机构：

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[2] Indiana Univ Purdue Univ, Dept Math Sci, Indianapolis, IN 46202 USA

[3] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2013年 / 70卷

基金：

中国国家自然科学基金;

关键词：

Square metrics; Einstein-Douglas; Warped product; (ALPHA; BETA)-METRICS;

D O I：

10.1016/j.geomphys.2013.03.009

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 metrics defined by a Riemannian metric and a one-form on a manifold. We completely determine the local structure of Ricci-flat metrics in this class which are also of Douglas type. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：30 / 38

页数：9

共 14 条

[1]

Bacso S., 2007, Adv. Stud. Pure Math., Math. Soc. Japan, V48, P73

[2]

Bao D, 2004, J DIFFER GEOM, V66, P377

[3]

Bao D., 2004, Math. Sci. Res. Inst. Publ., V50, P197

[4]

Bao D., 2000, An Introduction to Riemann-Finsler Geometry

[5] UEBER FINSLERSCHE UND CARTANSCHE GEOMETRIE .4. PROJEKTIVKRUMMUNG ALLGEMEINER AFFINER RAUME UND FINSLERSCHE RAUME SKALARER KRUMMUNG [J].

BERWALD, L .

ANNALS OF MATHEMATICS, 1947, 48 (03) :755-781

[6] Einstein spaces which are mapped conformally on each other [J].

Brinkmann, HW .

MATHEMATISCHE ANNALEN, 1925, 94 :119-145

[7] A class of Einstein (α, β)-metrics [J].

Cheng, Xinyue ;

Shen, Zhongmin ;

Tian, Yanfang .

ISRAEL JOURNAL OF MATHEMATICS, 2012, 192 (01) :221-249

[8] ON A CLASS OF DOUGLAS METRICS [J].

Li, Benling ;

Shen, Yibing ;

Shen, Zhongmin .

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2009, 46 (03) :355-365

[9]

Petersen P., Warped Product

[10] ON A CLASS OF RICCI-FLAT DOUGLAS METRICS [J].

Sevim, Esra Sengelen ;

Shen, Zhongmin ;

Zhao, Lili .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2012, 23 (06)

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