Geodesic
On Projectively Flat (α, β)-metrics
Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 132-144

Voir la notice de l'article provenant de la source Cambridge University Press

The solutions to Hilbert's Fourth Problem in the regular case are projectively flat Finsler metrics. In this paper, we consider the so-called $\left( \alpha ,\,\beta\right)$ -metrics defined by a Riemannian metric $\alpha$ and a 1-form $\beta$ , and find a necessary and sufficient condition for such metrics to be projectively flat in dimension $n\,\ge \,3$ .
DOI : 10.4153/CMB-2009-016-2
Mots-clés : 53B40, 53C60 
Shen, Zhongmin. On Projectively Flat (α, β)-metrics. Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 132-144. doi: 10.4153/CMB-2009-016-2
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