GEODESIC VECTOR FIELDS OF INVARIANT (alpha, beta)-METRICS ON HOMOGENEOUS SPACES

被引：0
|
作者：
Parhizkar, M. [1 ]
Moghaddam, H. R. Salimi [2 ]
机构：
[1] Univ Mohaghech Ardabili, Dept Math, POB 56199-11367, Ardebil, Iran
[2] Univ Isfahan, Fac Sci, Dept Math, Esfahan 8174673441, Iran
来源：
INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY | 2013年 / 6卷 / 02期
关键词：
homogeneous space; invariant Riemannian metric; invariant(alpha; beta)-metric;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we show that for an invariant (alpha, beta)-metric F on a homogeneous Finsler manifold G/H, induced by an invariant Riemannian metric (a) over tilde and an invariant vector field (X) over tilde the vector X = (X) over tilde (H) is a geodesic vector of F if and only if it is a geodesic vector of (a) over tilde. Then we give some conditions such that under them, an arbitrary vector is a geodesic vector of F if and only if it is a geodesic vector of (a) over tilde. Finally we give an explicit formula for the flag curvature of bi-invariant (alpha, beta)-metrics on connected Lie group.
引用
收藏
页码：39 / 44
页数：6
相关论文
共 50 条
  • [1] Invariant geodesic orbit metrics on certain compact homogeneous spaces
    Chen, Huibin
    Chen, Zhiqi
    Yan, Zaili
    Zhu, Fuhai
    [J]. MANUSCRIPTA MATHEMATICA, 2023, 172 (3-4) : 651 - 668
  • [2] Invariant geodesic orbit metrics on certain compact homogeneous spaces
    Huibin Chen
    Zhiqi Chen
    Zaili Yan
    Fuhai Zhu
    [J]. manuscripta mathematica, 2023, 172 : 651 - 668
  • [3] INVARIANT MATSUMOTO METRICS ON HOMOGENEOUS SPACES
    Moghaddam, H. R. Salimi
    [J]. OSAKA JOURNAL OF MATHEMATICS, 2014, 51 (01) : 39 - 45
  • [4] INVARIANT FINSLER METRICS ON POLAR HOMOGENEOUS SPACES
    Deng, Shaoqiang
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 2010, 247 (01) : 47 - 74
  • [5] CONFORMALLY RELATED INVARIANT (α, β)-METRICS ON HOMOGENEOUS SPACES
    Fatahi, Azar
    Hosseini, Masoumeh
    Moghaddam, Hamid Reza Salimi
    [J]. QUAESTIONES MATHEMATICAE, 2024, 47 (08) : 1559 - 1570
  • [6] Geodesic Mappings of Spaces with φ(Ric) Vector Fields
    Vashpanov, Y.
    Olshevska, O.
    Lesechko, O.
    [J]. APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES (AMITANS 2020), 2020, 2302
  • [7] Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spaces
    Chen, Huibin
    Chen, Zhiqi
    Zhu, Fuhai
    [J]. SCIENCE CHINA-MATHEMATICS, 2021, 64 (10) : 2313 - 2326
  • [8] Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spaces
    Huibin Chen
    Zhiqi Chen
    Fuhai Zhu
    [J]. Science China Mathematics, 2021, 64 : 2313 - 2326
  • [9] Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spaces
    Huibin Chen
    Zhiqi Chen
    Fuhai Zhu
    [J]. Science China Mathematics, 2021, 64 (10) : 2313 - 2326
  • [10] Invariant naturally reductive Randers metrics on homogeneous spaces
    Late, Dariush
    Toomanian, Megerdich
    [J]. MATHEMATICAL SCIENCES, 2012, 6 (01)
12345