On Naturally Reductive $\boldsymbol{(\alpha_1,\alpha_2)}$-Metrics

Ali Hatami Shahi; Hamid Reza Salimi Moghaddam

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arXiv · 2602.15035

On Naturally Reductive $\boldsymbol{(\alpha_1,\alpha_2)}$-Metrics

Ali Hatami Shahi·Hamid Reza Salimi Moghaddam

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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 $(\alpha_1,\alpha_2)$-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 $(\alpha_1,\alpha_2)$-spaces. Finally, we construct left-invariant $(\alpha_1,\alpha_2)$-metrics on the tangent bundle of Lie groups using left-invariant Randers metrics on the base Lie group, and study their geometric relations.

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BibTeX RIS

Ali Hatami Shahi, Hamid Reza Salimi Moghaddam. 2026-01-24. On Naturally Reductive $\boldsymbol{(\alpha_1,\alpha_2)}$-Metrics. https://arxiv.org/abs/2602.15035

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