On locally dually flat (α,β)(α,β)-metrics

The notion of locally dually flat Finsler metrics are originated from information geometry. Some special locally dually flat Finsler metrics had been studied in Cheng et al. (2009) (in press) [6] and Xia (in press) [10] respectively. As we know, (α,β)(α,β)-metrics defined by a Riemannian metric α and a 1-form β   form an important class of Finsler metrics. In this paper, we study and give a characterization of locally dually flat (α,βα,β)-metrics on an n-dimensional manifold M  (n⩾3)(n⩾3), which generalizes some results in Cheng et al. (2009) (in press) [6] and Xia (in press) [10].