On a new class of Finsler metrics

Abstract In this paper, the geometric meaning of ( α , β ) -norms is made clear. On this basis, a new class of Finsler metrics called general ( α , β ) -metrics are introduced, which are defined by a Riemannian metric and a 1-form. These metrics not only generalize ( α , β ) -metrics naturally, but also include some metrics structured by R. Bryant. The spray coefficients formula of some kinds of general ( α , β ) -metrics is given and the projective flatness is also discussed.