局部射影平坦Berwald型(α, β)度量的一个刻画

A Characterization for Locally Projectively Flat Berwald Type (α, β)-Metrics

摘要: Berwald型(α, β)度量是形如F=(α, β)²/a的芬斯勒度量，其中α是一个黎曼度量，β是一个1形式。本文利用β对α和β做一种特殊的度量形变，由此可以得到局部射影平坦Berwald型 (α, β)度量的一个刻画。该刻画不仅比其他研究者的相应方法和结论简单，而且从中我们可以看到局部射影平坦Berwald型(α, β)度量更为明确的几何结构。

Abstract: Berwald type (α, β)-metrics are those Finsler metrics expressed as F=(α, β)²/a, where α is a Riemannian metric, and β is a 1-form. In this paper, by using a special deformations for α and β due to β, we provide a characterization for locally projectively flat Berwald tpye (α, β)-metrics. Our characterization is simpler than the corresponding results of other researchers. Moreover, the geometrical structure of locally projectively flat Berwald type (α, β)-metrics is much clearer.