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Mathematics > Differential Geometry
Title: Existence theorem for sub-Lorentzian problems
(Submitted on 15 Jan 2024 (v1), last revised 13 May 2024 (this version, v2))
Abstract: In this paper, we prove the existence theorem for longest paths in sub-Lorentzian problems, which generalizes the classical theorem for globally hyperbolic Lorentzian manifolds. We specifically address the case of invariant structures on homogeneous spaces, as the conditions for the existence theorem in this case can be significantly simplified. In particular, it turns out that longest paths exist for any left-invariant sub-Lorentzian structures on Carnot groups.
Submission history
From: Alexey Podobryaev [view email][v1] Mon, 15 Jan 2024 21:42:47 GMT (13kb)
[v2] Mon, 13 May 2024 17:32:03 GMT (13kb)
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