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arXiv · 1305.2862

Flag curvature of invariant $(\alpha,\beta)$-metrics of type $\frac{(\alpha+\beta)^2}{\alpha}$

H. R. Salimi Moghaddam
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Abstract

In this paper we study flag curvature of invariant $(\alpha,\beta)$-metrics of the form $\frac{(\alpha+\beta)^2}{\alpha}$ on homogeneous spaces and Lie groups. We give a formula for flag curvature of invariant metrics of the form $F=\frac{(\alpha+\beta)^2}{\alpha}$ such that $\alpha$ is induced by an invariant Riemannian metric $g$ on the homogeneous space and the Chern connection of $F$ coincides to the Levi-Civita connection of $g$. Then some conclusions in the cases of naturally reductive homogeneous spaces and Lie groups are given.

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H. R. Salimi Moghaddam. 2013-05-01. Flag curvature of invariant $(\alpha,\beta)$-metrics of type $\frac{(\alpha+\beta)^2}{\alpha}$. https://doi.org/10.1088/1751-8113/41/27/275206

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