On Conformally Flat Exponential (alpha, beta)-Metrics

摘要

Let F be a conformally flat exponential (alpha, beta)-metric on a manifold of dimension n >= 3. In this paper, we prove that if F is a weakly Einstein metric, then it is either a Riemannian metric or a locally Minkowski metric. If F has almost vanishing Xi-curvature, then it is a Riemannian metric or a locally Minkowski metric. If F has relatively isotropic mean Landsberg curvature, then it is either a Riemannian metric or a locally Minkowski metric.