The geometric structure of the bivariate q-normal distribution manifold

In this paper, we investigate the geometric structure of the bivariate g-normal distribution manifold (S) which consists of all bivariate g -normal probability density functions. By introducing g -operator and g -potential function, the curvature tensor of the manifold S is obtained. Meanwhile, we get the dual coordinate systems of S. Further, we investigate the geometric structures of its submanifolds, and give their dual coordinate systems and scalar curvatures. Using the g Kullback-Leibler divergence, projections are defined from the bivariate g -normal distribution manifold to its submanifolds. Finally, there is an example to illustrate our conclusions.