ON SEMI-C-REDUCIBILITY OF (α, β)-METRICS

Abstract

Every non-Riemannian (α, β)-metric on a manifold with dimension n ≥ 3 is semi-C-reducible. Thus the study on semi-C-reducible metrics will enhance our understanding on the physical meaning of (α, β)-metrics. In this paper, we study weakly Landsberg semi-C-reducible metrics with some non-Riemannian curvature properties. Then we find some conditions on semi-C-reducible manifolds under which the notions of isotropic Landsberg curvature and of isotropic mean Landsberg curvature are equivalent.