Properties of Berwald scalar curvature

Abstract

We prove that a Finsler manifold with vanishing Berwald scalar curvature has zero E-curvature. As a consequence, Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds. For (α,β)-metrics on manifold of dimension greater than 2, if the mean Landsberg curvature and the Berwald scalar curvature both vanish, then the Berwald curvature also vanishes.

Keywords

Landsberg curvature / Berwald curvature / E-curvature / S-curvature Berwald scalar curvature

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