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On the flag curvature of invariant $(α, β)$ -metrics

M. Parhizkar

Department of Mathematics, University of Mohaghegh Ardabili, P. O. Box. 5619911367, Ardabil, Iran

E-mail Address: m.parhizkar@uma.ac.ir

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and

D. Latifi

Department of Mathematics, University of Mohaghegh Ardabili, P. O. Box. 5619911367, Ardabil, Iran

E-mail Address: latifi@uma.ac.ir

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https://doi.org/10.1142/S0219887816500390Cited by:4 (Source: Crossref)

Abstract

In this paper, we consider invariant $(α, β)$ -metrics which are induced by invariant Riemannian metrics $ã$ and invariant vector fields $\tilde{X}$ on homogeneous spaces. We study the flag curvatures of invariant $(α, β)$ -metrics. We first give an explicit formula for the flag curvature of invariant $(α, β)$ -metrics arising from invariant Riemannian metrics on homogeneous spaces and Lie groups. We then give some explicit formula for the flag curvature of invariant Matsumoto metrics, invariant Kropina metrics and invariant Randers metrics.

Keywords:

AMSC: 53C60, 53C30

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