左不变三维接触子洛伦兹结构中最长弧的存在性
Existence of the longest arcs for left-invariant three-dimensional contact sub-Lorentzian structures
AI总结：
本文研究了左不变三维接触子洛伦兹结构中最长弧的存在性，提出了在可解李群和SL(2, R)李群 universal cover 上的充分存在条件。
摘要：
寻找子洛伦兹结构的最优曲线（最长弧）是一个具有无界控制集和凹成本函数的最优控制问题。此类问题的最优解存在性并不平凡。本文针对某些已知分类的左不变三维接触子洛伦兹结构，解决了这一问题。我们为左不变（子）洛伦兹结构在可解李群和SL(2, R)李群的 universal cover 上提出存在最长弧的充分条件。
英文摘要：
The problem of finding optimal curves (the longest arcs) for sub-Lorentzian structures is an optimal control problem with an unbounded control set and a concave cost functional. The question of existence of an optimal solution is nontrivial for such problems. We solve here this question for some left-invariant three-dimensional contact sub-Lorentzian structures, whose classification is known. We propose sufficient conditions for the existence of the longest arcs for left-invariant (sub-)Lorentzian structures on solvable Lie groups and on the universal cover of the Lie group SL(2, R).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
