Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

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

Articles in Press

Document Type : Research Article

Authors
Ali Hatami Shahi 1
Hamid Reza Salimi Moghaddam 2
1 Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, Iran.
2 Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan.
10.30504/jims.2026.578080.1328
Abstract
In this article, we show that if $(M=G/H,g)$ is a naturally reductive homogeneous Riemannian manifold and $\frak{g}' \subset \frak{h}+\frak{m}_1$, then the $(\alpha_1,\alpha_2)$-metric $F$ induced by $g$ and the decomposition $\frak{m}=\frak{m}_1+\frak{m}_2$ is also naturally reductive. To establish this, we provide an explicit formula for the Cartan tensor of homogeneous $(\alpha_1,\alpha_2)$-metrics. We further examine the relationship between geodesic vector fields on homogeneous Riemannian spaces and their counterparts on homogeneous $(\alpha_1,\alpha_2)$-spaces. Finally, we construct left-invariant $(\alpha_1,\alpha_2)$-metrics on the tangent bundle of Lie groups from left-invariant Randers metrics on the base Lie group and study their geometric relations.
Keywords
(\alpha_1,\alpha_2)-Metric
Randers metric
Naturally reductive
Tangent Lie group
Subjects
Journal of the Iranian Mathematical Society

Articles in Press, Accepted Manuscript
Available Online from 22 July 2026