Classification of ۲-Dimensional Bryant-Type Metrics

The class of Bryant-type metrics is a  natural extension of the class of ۴-th root Finsler metrics which are used in Biology as ecological metrics. In this paper, we  classify  Bryant-type metrics admitting an (alpha, beta)-metric on a two-dimensional  manifold and show that it contains two classes of non-Riemannian (alpha, beta)-metrics, specially Randers-type metrics. This might provide fine insights into a possible theory of deformations of Finsler norms.

کلیدواژه ها:

Bryant metric ، generalized ۴-th root metric ، ۴-th root metric ، (alpha ، beta)-metric ، Randers-type metric.