ON LOCALLY DUALLY FLAT GENERALIZED BERWALD (α, β)-MANIFOLDS

The base of information geometry come back to the interesting and seminal work of Rao
in 1992, where he considered the Fisher matrix as a Riemannian metric. But the modern
theory is due to the Amari's lecture notes in statistics, whose work has been major influential
on the development of the field. In information geometry, a parametrized statistical
model considered as a Riemannian manifold. For such models, there is a natural choice
of Riemannian metric, known as the Fisher information metric. Information geometry has
emerged from investigating the geometrical structure of a family of probability distributions
and has been applied successfully to various areas including statistical inference, control system theory and multi-terminal information theory.
Locally dually flat Finsler metrics form an interesting class of Finsler metrics in Finsler information geometry. Every locally Minkowskian metric is locally dually flat. But there are many locally dually flat metrics that are not locally Minkowskian. In this paper, we study the class of locally dually flat generalized Berwald (α, β)-metrics and find the conditions under which these metrics reduce to locally Minkowskian.