On left-invariant Einstein metrics that are not geodesic orbit

被引:2
作者
Xu, Na [1 ]
Tan, Ju [1 ]
机构
[1] Anhui Univ Technol, Sch Math & Phys, Maanshan 243032, Peoples R China
关键词
LIE-GROUPS;
D O I
10.1016/j.crma.2019.07.003
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this article, we prove that compact simple Lie groups SO(n) (n > 12) admit at least two left-invariant Einstein metrics that are not geodesic orbit, which gives a positive answer to a problem recently posed by Nikonorov. (C) 2019 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
引用
收藏
页码:624 / 628
页数:5
相关论文
共 9 条
  • [1] Einstein metrics on compact Lie groups which are not naturally reductive
    Arvanitoyeorgos, Andreas
    Mori, Kunihiko
    Sakane, Yusuke
    [J]. GEOMETRIAE DEDICATA, 2012, 160 (01) : 261 - 285
  • [2] Compact simple Lie groups admitting left-invariant Einstein metrics that are not geodesic orbit
    Chen, Huibin
    Chen, Zhiqi
    Deng, Shaoqiang
    [J]. COMPTES RENDUS MATHEMATIQUE, 2018, 356 (01) : 81 - 84
  • [3] Chen ZQ, 2014, ANN GLOB ANAL GEOM, V46, P103, DOI 10.1007/s10455-014-9413-5
  • [4] Non-naturally reductive Einstein metrics on exceptional Lie groups
    Chrysikos, Ioannis
    Sakane, Yusuke
    [J]. JOURNAL OF GEOMETRY AND PHYSICS, 2017, 116 : 152 - 186
  • [5] KOWALSKI O, 1991, B UNIONE MAT ITAL, V5B, P189
  • [6] ON LEFT-INVARIANT EINSTEIN RIEMANNIAN METRICS THAT ARE NOT GEODESIC ORBIT
    Nikonorov, Yu. G.
    [J]. TRANSFORMATION GROUPS, 2019, 24 (02) : 511 - 530
  • [7] Homogeneous Einstein-Randers metrics on symplectic groups
    Tan, Ju
    Xu, Na
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 472 (02) : 1902 - 1913
  • [8] EINSTEIN METRICS ON COMPACT SIMPLE LIE GROUPS ATTACHED TO STANDARD TRIPLES
    Yan, Zaili
    Deng, Shaoqiang
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 369 (12) : 8587 - 8605
  • [9] New non-naturally reductive Einstein metrics on SO(n)
    Zhang, Ho
    Chen, Huibin
    Tan, Ju
    [J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2018, 29 (11)