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On the Pontrjagin classes of spray manifolds
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- Journal:
- Canadian Mathematical Bulletin / Volume 67 / Issue 3 / September 2024
- Published online by Cambridge University Press:
- 11 December 2023, pp. 544-553
- Print publication:
- September 2024
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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.
