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

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DOI

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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     title = {On {Projectively} {Flat} (\ensuremath{\alpha}, \ensuremath{\beta})-metrics},
     journal = {Canadian mathematical bulletin},
     pages = {132--144},
     year = {2009},
     volume = {52},
     number = {1},
     doi = {10.4153/CMB-2009-016-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-016-2/}
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