Some Properties Of Finsler Metric With Generalized Isotropic Berwald Curvature And A Class Of Special (α,β)-Metric

In this paper, we study some properties of Finsler metric with generalized isotropic Berwald curvature and a class of special (α,β )-metric. Using Maple programme,we figure out the geodesic coefficients and the mean Cartan torsions of (α,β)-metrics in the third part; We discuss con-ditions of F = αe~kβ/α metric to be Berwald, Douglas, Projectively flat, and get an additional formula which is used to calculate Douglas curvature in the fourth part; On the basis of introducing generalized isotropic Berwald curvature, we find two sufficient and necessary conditions of generalized isotropic Berwald curvature in the fifth part. We obtain mainly the following results:Proposition 3.6 The det(gij), the geodesic coefficients and the mean Cartan torsions of F = αe~kβ/α of (α,β)-metrics that k is constant are:...