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arXiv · 2211.16435

On the Pontrjagin classes of spray manifolds

Zhongmin Shen·Runzhong Zhao
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Abstract

Locally projectively flat metrics (or sprays) form a rich class of metrics (or sprays) in Finsler and spray geometry. The characterization of such metrics is the Hilbert Fourth Problem in the regular case. In this paper we study the Pontrjagin classes of a manifold given a spray structure, and show that a manifold equipped with a locally projectively flat Finsler metric (or spray) has zero Pontrjagin classes.

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Zhongmin Shen, Runzhong Zhao. 2022-11-29. On the Pontrjagin classes of spray manifolds. https://doi.org/10.4153/s0008439523000954

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