Scholarlink

<p>In this article, we prove that every compact simple Lie group SO(3<i>k</i>+ 2) (<i>k</i> ≥ 6) admits at least two non-naturally reductive Ad(SO(<i>k</i>) × SO(<i>k</i> + 1) × SO(<i>k</i> + 1))-invariant Einstein metrics, and prove that there are at least two non-naturally reductive Einstein metrics on compact simple Lie group SO(8<i>n</i>) (<i>n</i> ≥ 26), which are Ad(SO(2<i>n</i>) × SO(3<i>n</i>) × SO(3<i>n</i>))-invariant. Besides, we prove that the two non-naturally reductive Ad(SO(<i>k</i>) × SO(<i>k</i> +1) × SO(<i>k</i> + 1))-invariant Einstein metrics are also non-geodesic orbit. Finally, we obtain two non-geodesic orbit Einstein–Randers metrics on SO(3<i>k</i> + 2) (<i>k</i> ≥ 6).</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Non-geodesic Orbit Einstein–Randers Metrics on SO(n)

  • 期刊论文

  • 发表日期：

    2026年7月5日

查看全文
  • Mengxue Zhang,
  • Ju Tan,
  • Na Xu

摘要

In this article, we prove that every compact simple Lie group SO(3k+ 2) (k ≥ 6) admits at least two non-naturally reductive Ad(SO(k) × SO(k + 1) × SO(k + 1))-invariant Einstein metrics, and prove that there are at least two non-naturally reductive Einstein metrics on compact simple Lie group SO(8n) (n ≥ 26), which are Ad(SO(2n) × SO(3n) × SO(3n))-invariant. Besides, we prove that the two non-naturally reductive Ad(SO(k) × SO(k +1) × SO(k + 1))-invariant Einstein metrics are also non-geodesic orbit. Finally, we obtain two non-geodesic orbit Einstein–Randers metrics on SO(3k + 2) (k ≥ 6).