Geodesic
On the Pontrjagin classes of spray manifolds
Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 544-553

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The characterization of projectively flat Finsler metrics on an open subset in $R^n$ is the Hilbert’s fourth problem in the regular case. Locally projectively flat Finsler manifolds form an important class of Finsler manifolds. Every Finsler metric induces a spray on the manifold via geodesics. Therefore, it is a natural problem to investigate the geometric and topological properties of manifolds equipped with a spray. In this paper, we study the Pontrjagin classes of a manifold equipped with a locally projectively flat spray and show that such manifold must have zero Pontrjagin classes.
DOI : 10.4153/S0008439523000954
Mots-clés : spray geometry, Pontrjagin class, projectively flat sprays, Douglas sprays 
Shen, Zhongmin; Zhao, Runzhong. On the Pontrjagin classes of spray manifolds. Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 544-553. doi: 10.4153/S0008439523000954
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     title = {On the {Pontrjagin} classes of spray manifolds},
     journal = {Canadian mathematical bulletin},
     pages = {544--553},
     year = {2024},
     volume = {67},
     number = {3},
     doi = {10.4153/S0008439523000954},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000954/}
}
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