Geodesic Orbit Metrics on Compact Simple Lie Groups arising from Generalized Flag Manifolds

TL;DR

This paper proves that all left-invariant geodesic orbit metrics on connected simple Lie groups, constructed via generalized flag manifolds, are inherently naturally reductive, advancing understanding of geometric structures on Lie groups.

Contribution

It establishes that such metrics are always naturally reductive, providing a comprehensive classification for this class of metrics on simple Lie groups.

Findings

All studied metrics are naturally reductive.

The metrics are constructed from generalized flag manifolds.

The result applies to connected simple Lie groups.

Abstract

In this paper, we investigate left-invariant geodesic orbit metrics on connected simple Lie groups, where the metrics are formed by the structures of generalized flag manifolds. We prove that all these left-invariant geodesic orbit metrics on simple Lie groups are naturally reductive.