On the space of cone geodesics and positive paths of contactomorphisms

Jakob Hedicke

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arXiv · 2512.20149

On the space of cone geodesics and positive paths of contactomorphisms

Jakob Hedicke

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Abstract

Often it is possible to equip the space of all cone geodesics of a strongly convex cone structure with the structure of a smooth contact manifold. This generalizes the analogous notions for the space of light rays of a Lorentzian spacetime. After reviewing these constructions on the space of cone geodesics, with a focus on the natural contact structure, we establish a correspondence between positive paths of contactomorphisms in spherical cotangent bundles and certain globally hyperbolic cone structures.

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Jakob Hedicke. 2025-12-23. On the space of cone geodesics and positive paths of contactomorphisms. https://arxiv.org/abs/2512.20149

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