Abstract
Let ( M , L ) be a pseudo-Finsler manifold, ξ the geodesic spray vector field associated to the non-degenerate, 2-positively homogeneous Lagrangian L . In this paper we prove that ( M , L ) is of scalar flag curvature k if and only if the equation L ξ g + k λ L ξ g ˆ = 0 holds on Γ ( I λ M ) , the Lie algebra of tangent vector fields to the λ -indicatrix bundle I λ M , where g and g ˆ are pseudo-Riemannian metrics on the vertical and respectively on the horizontal subbundle. Also, we prove that any pseudo-Finsler manifold is of scalar flag curvature at any point of the light cone.
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