Properties of the Absolute That Affect Smoothness of Flows on Closed Surfaces |
| |
Authors: | S Kh Aranson E V Zhuzhoma |
| |
Institution: | (1) Nizhnii Novgorod State Technical University, Russia;(2) Nizhnii Novgorod State Technical University, Russia |
| |
Abstract: | Let
be a closed orientable surface of genus
, endowed with the structure of a Riemann manifold of constant negative curvature. For the universal covering
, there is the notion of absolute, each of whose points determines an asymptotic direction of a bundle of parallel equidirected geodesics. In the paper it is proved that there is a set
on the absolute having the cardinality of the continuum and such that if an arbitrary flow on
has a semitrajectory whose covering has asymptotic direction defined by a point from
, then this flow is not analytical and has infinitely many stationary points. |
| |
Keywords: | flow closed orientable surface foliation geodesic universal covering Lobachevskii plane absolute asymptotic direction |
本文献已被 SpringerLink 等数据库收录! |