A Class Of Generalized (α, β) - Some Of The Results Measured

In this paper,we study a class of Finsler metrics called general (α,β)-metrics,which are de-fined by a Riemannian metric a and1-from β. When β satisfies bi|j=c(aij-λbibj),we obtain the sufficient and necessary conditions which F is projectively equivalent to a and F is a Douglas metric respectively. What’s more, if a is projectively flat and F is projectively equivalent to α, then F is projectively flat metric. Besides,we also study the Einstein characteristics of this class of metrics.When a is Einstein metrics,β satisfies bi|j=c(aij-λbibj) and F is projectively equivalent to α,we give a characterization of general (α,β)-metrics with constant Ricci curvature. In partic-ular,if a is Ricci-flat.then we give a classification of Einstein general (α,β)-metrics with constant Ricci curvature.Finally,we also construct some Ricci-flat general (α,β)-metrics of Berwald type.