On a class of locally dually flat (α, β )-metric Rishabh Ranjan, P. N. Pandey and Ajit Paul Abstract. In this paper, we discuss a class of locally dually flat (α,β)- metrics which are defined as L = κα + ϵβ (κ and ϵ are constants), where α is Riemannian metric and β is 1-form. We classify those with almost isotropic flag curvature. M.S.C. 2010: 53B40, 53C60. Key words: Finsler metric, locally dually flat, flag curvature, Riemannian metric. 1 Introduction M. Matsumoto [9] introduced the concept of (α,β)-metric on a differentiable manifold M n , where α 2 = a ij (x)y i y j is a Riemannian metric and β = b i (x)y i is a 1-form. The Matsumoto metric is an interesting (α,β)-metric introduced by using gradient of slope, speed and gravity [8]. This metric formulates the model of a Finsler space. Many authors [8, 1, 11] studied this metric by different perspectives. The notion of dually flat metrics was first introduced by S. I. Amari and H. Nagaoka [2]. Later on, Zhongmin Shen [14] extends the notion of dually flatness to Finsler metrics. In particular, Zhongmin Shen [15] has classified projectively flat Randers metrics with constant flag curvature. In 2009, X. Cheng, Z. Shen and Y. Zhou [4] classified the locally dual flat Randers metrics with almost isotropic flag curvature. Recently, Q. Xia worked on the dual flatness of Finsler metrics of isotropic flag cur- vature as well as scalar flag curvature [16]. Further in 2014, S. K. Narasimhamurthy, A. R. kavyashree and Y. K. Mallikarjun [10] discuss characterization of locally dually flat first approximate Matsumoto metric. Locally dually flat Finsler metrics come from information Geometry. Such metrics have very important geometric properties and can play vital role in Finsler Geometry. In this paper, we discussed a class of locally dually flat (α,β)-metrics which are defined as L = κα + ϵβ (κ and ϵ are con- stants), where α is Riemannian metric and β is 1-form. We classify those with almost isotropic flag curvature. Differential Geometry - Dynamical Systems, Vol.22, 2020, pp. 208-217. c ⃝ Balkan Society of Geometers, Geometry Balkan Press 2020.