给定类型测地线在单位切丛中的分布
Distribution in the unit tangent bundle of the geodesics of given type
摘要：
回想一下，负曲面$S$中的两条测地线是同一类型的，如果它们的自由同伦类因曲面的同胚而不同。本文研究了固定型测地线在单位切丛中的分布，证明了它们关于$T^1S$上的某个测度$\mathfrak{m}^S$是渐近等分布的.我们研究的一些性质，这种措施，例如，它区分双曲曲面。
英文摘要：
Recall that two geodesics in a negatively curved surface $S$ are of the same type if their free homotopy classes differ by a homeomorphism of the surface. In this note we study the distribution in the unit tangent bundle of the geodesics of fixed type, proving that they are asymptotically equidistributed with respect to a certain measure $\mathfrak{m}^S$ on $T^1S$. We study a few properties of this measure, showing for example that it distinguishes between hyperbolic surfaces.
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。
