J4 ›› 2010, Vol. 45 ›› Issue (4): 39-42.

• Articles • Previous Articles     Next Articles

A note on the collars in complex hyperbolic manifolds

LI Na, LI Chang-jun*   

  1. School of Mathematical Sciences, Ocean University of China, Qingdao 266071, Shandong, China
  • Received:2009-07-15 Online:2010-04-10 Published:2010-05-19

Abstract:

The relationships between  the length of the axes of a loxodromic element and the existence of a precisely invariant tube about the axis are studied. The volume of the embedded collar about a geodesic is obtained. Finally, the lower bound of the minimum distance between two distinct, short, simple, closed geodesics in a complex hyperbolic 2-manifold is given.
 

Key words: geodesic; collars; tube

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