A class of Einstein (α, β)-metrics

被引：30
|
作者：
Cheng, Xinyue [1 ]
Shen, Zhongmin [2 ]
Tian, Yanfang [1 ,3 ]
机构：
[1] Chongqing Univ Technol, Sch Math & Stat, Chongqing 400054, Peoples R China
[2] Indiana Univ Purdue Univ, Dept Math Sci, Indianapolis, IN 46202 USA
[3] Logist Engn Univ PLA, Chongqing 400016, Peoples R China
来源：
ISRAEL JOURNAL OF MATHEMATICS | 2012年 / 192卷 / 01期
关键词：
Sectional Curvature; Ricci Curvature; Einstein Metrics; Riemann Curvature; Finsler Space;
D O I：
10.1007/s11856-012-0036-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study a special class of Finsler metrics, called (alpha, beta)-metrics, which are defined by F = alpha I center dot(beta/alpha), where alpha is a Riemannian metric and beta is a 1-form. We show that if I center dot = I center dot(s) is a polynomial in s, it is Einstein if and only if it is Ricci-flat. We also determine the Ricci-flat (alpha, beta)-metrics which are not of the type F = (alpha + E >beta)(2)/alpha.
引用
收藏
页码：221 / 249
页数：29
相关论文
共 50 条
  • [31] On Einstein Matsumoto metrics
    XiaoLing Zhang
    QiaoLing Xia
    Science China Mathematics, 2014, 57 : 1517 - 1524
  • [32] On Einstein Finsler metrics
    Ulgen, Semail
    Sevim, Esra Sengelen
    Hacinliyan, Irma
    INTERNATIONAL JOURNAL OF MATHEMATICS, 2021, 32 (09)
  • [33] Unstable Einstein metrics
    Christoph Böhm
    Mathematische Zeitschrift, 2005, 250 : 279 - 286
  • [34] On homogeneous Einstein (α,β)-metrics
    Yan, Zaili
    Deng, Shaoqiang
    JOURNAL OF GEOMETRY AND PHYSICS, 2016, 103 : 20 - 36
  • [35] On Einstein square metrics
    Shen, Zhongmin
    Yu, Changtao
    PUBLICATIONES MATHEMATICAE-DEBRECEN, 2014, 85 (3-4): : 413 - 424
  • [36] On Einstein Matsumoto metrics
    Rafie-Rad, M.
    Rezaei, B.
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (02) : 882 - 886
  • [37] Einstein Landsberg metrics
    Sadeghzadeh, Nasrin
    Razavi, Asadollah
    Rezaei, Barman
    PUBLICATIONES MATHEMATICAE-DEBRECEN, 2009, 75 (3-4): : 311 - 326
  • [38] On generalized Einstein metrics
    Labbi, Mohammed Larbi
    BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS, 2010, 15 (02): : 69 - 77
  • [39] New pseudo Einstein metrics on Einstein solvmanifolds
    Hui Zhang
    Zaili Yan
    manuscripta mathematica, 2021, 166 : 427 - 436
  • [40] New pseudo Einstein metrics on Einstein solvmanifolds
    Zhang, Hui
    Yan, Zaili
    MANUSCRIPTA MATHEMATICA, 2021, 166 (3-4) : 427 - 436
12345