On a new class of Finsler metrics

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