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arXiv · 2608.12907

Rigidity theorems for cone structures

Tymon Frelik·Wojciech Kryński
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Abstract

Cone structures on differentiable manifolds are fields of cones in the tangent bundle. A cone structure is isotrivial, modeled on a fixed immersed submanifold of the projective space, if at each point the projectivised cone is projectively equivalent to that submanifold. We consider cone structures arising from ordinary differential equations via a canonical construction. We prove that isotrivial cone structures in this class, modeled on generic curves in the $n$-dimensional projective space or ruled surfaces in the three-dimensional projective space, are flat. We also discuss applications to causal geometries in four dimensions and dispersionless Lax systems.

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BibTeXRIS

Tymon Frelik, Wojciech Kryński. 2026-08-13. Rigidity theorems for cone structures. https://arxiv.org/abs/2608.12907

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