Classification of three-dimensional left-invariant Ricci-quadratic Randers metrics and their applications

In this paper, we determine the necessary and sufficient conditions for a left-invariant Randers metric to be a Ricci-quadratic metric. Then, by using HaBumlee’s classification of left-invariant Riemannian metrics and our characterization of Ricci-quadratic left-invariant Randers metrics, we give the classification of left-invariant Ricci-quadratic Randers metrics on three-dimensional Lie groups. As an application, we find an interesting Ricci-quadratic Randers metric on  SU(۲) which is a generalized Berwald metric, while it is not Berwaldian. Also, we prove that it is a generalized Douglas-Weyl metric which is neither Douglasian nor a Weyl metric.

کلیدواژه ها:

Left-invariant metric ، Randers metric ، Ricci-quadratic metric ، Berwald metric