Changtao Yu

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.

On Einstein square metrics

In this paper, we study an important class of Finsler metrics--square metrics. We give two expressions of such metrics in terms of a Riemannian metric and a 1-form. We show that Einstein square metrics can be classified up to the classification of Einstein Riemannian metrics.

Deformations and Hilbert’s fourth problem

In this paper a special class of Finsler metrics defined by a Riemannian metric and an 1-form is studied. The projectively flat metrics in dimension

On dually flat Randers metrics

n\ge 3

On dually flat (α,β)-metrics

n≥3 are classified by a new class of metric deformations in Riemann geometry. The results show that the projective flatness of such Finsler metrics always arises from that of some Riemannian metric.

On dually flat general (α,β)-metrics

In this paper, we study Finsler metrics expressed in terms of a Riemannian metric, an 1-form, and its norm. We find equations which are sufficient conditions for such Finsler metrics to have constant Ricci curvature. Using certain transformations, we successfully solve these equations and hence construct a large class of Einstein metrics.