English

Geodesics on adjoint orbits of $SL(n, \mathbb{R})$

Differential Geometry 2022-03-11 v1

Abstract

In this paper we study geodesics on adjoint orbits of SL(n,R)SL(n,\mathbb{R}) equipped with SO(n)SO(n)-invariant metrics (maximal compact subgroup). Our main technique is translate this problem into a geometric problem in the tangent bundle of certain SO(n)SO(n)-flag manifolds and describe the geodesics equations with respect to the Sasaki metric on tangent bundle. We also use tools of Lie Theory in order to obtain some explicit description of families of geodesics. We deal with the case of SL(2,R)SL(2,\mathbb{R}) in full details.

Keywords

Cite

@article{arxiv.2203.05514,
  title  = {Geodesics on adjoint orbits of $SL(n, \mathbb{R})$},
  author = {Rafaela F. do Prado and Brian Grajales and Lino Grama},
  journal= {arXiv preprint arXiv:2203.05514},
  year   = {2022}
}
R2 v1 2026-06-24T10:08:58.801Z