Work

Non-naturally reductive Einstein metrics on SO(n)

Year: 2025

Type: article

Abstract: In this article, we obtain that the compact simple Lie group S O ( 4 k + 3 ) ( k ≥ 8 ) admits at least two new non-naturally reductive A d ( S O ( k + 1 ) × S O ( k + 1 ) × S O ( k + 1 ) × S O ( k ) ) -invariant Einstein metrics, and the compact simple Lie group S O ( 4 k + 6 ) ( k ≥ 11 ) admits at least two new non-naturally reductive A d ( S O ( k + 2 ) × S O ( k + 2 ) × S O ( k + 2 ) × S O ( k ) ) -invariant Einstein metrics. Furthermore, we explore the isometry problem for these Einstein metrics. Finally, we prove that there are at least two families of non-naturally reductive invariant Einstein-Randers metrics on S O ( n ) ( n ≥ 35 ) and S O ( n ) ( n ≥ 50 ) respectively.

Source: Differential Geometry and its Applications

DOI: 10.1016/j.difgeo.2025.102294

Authors: Ming Wu, Ju Tan, Na Xu

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,740

Funders: National Natural Science Foundation of China, University Natural Science Research Project of Anhui Province

Awards: G4480549972, G8517765608