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

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.

References in corpus (1)

• Flag Curvature of Invariant Randers Metrics on Homogeneous Manifolds

Cited by in corpus (3)

• The Relation Between Automorphism Group and Isometry Group of Randers Lie Groups
• Randers Metrics of Berwald type on 4-dimensional hypercomplex Lie groups
• Naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces