On Naturally Reductive $\boldsymbol{(\alpha_1,\alpha_2)}$-Metrics
General Mathematics
2026-02-18 v1
Abstract
In this paper, we investigate the converse of the Tan-Xu theorem, which states that the naturally reductive property of a Riemannian metric is inherited by a naturally reductive -metric, and we show that, under certain conditions, the converse also holds. We also examine the relationship between geodesic vector fields on homogeneous Riemannian spaces and homogeneous -spaces. Finally, we construct left-invariant -metrics on the tangent bundle of Lie groups using left-invariant Randers metrics on the base Lie group, and study their geometric relations.
Keywords
Cite
@article{arxiv.2602.15035,
title = {On Naturally Reductive $\boldsymbol{(\alpha_1,\alpha_2)}$-Metrics},
author = {Ali Hatami Shahi and Hamid Reza Salimi Moghaddam},
journal= {arXiv preprint arXiv:2602.15035},
year = {2026}
}