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arXiv · 1602.06734

Non-existence of Funk functions for Finsler spaces of non-vanishing scalar flag curvature

Ioan Bucataru·Zoltán Muzsnay
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Abstract

In his book "Differential Geometry of Spray and Finsler spaces", page 177, Zhongmin Shen asks "wether or not there always exist non-trivial Funk functions on a spray space". In this note, we will prove that the answer is negative for the geodesic spray of a finslerian function of non-vanishing scalar flag curvature.

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Ioan Bucataru, Zoltán Muzsnay. 2016-02-22. Non-existence of Funk functions for Finsler spaces of non-vanishing scalar flag curvature. https://doi.org/10.1016/j.crma.2016.04.001

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