Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I want to understand the geometry of the Hyperbolic annuli (Hyperbolic plane quoteinted by the group generated by $z\mapsto rz$ for a fixed $r$) and parabolic annuli (Hyperbolic plane quoteinted by the group generated by $z\mapsto z + 1$). Some questions i want to understand are :Injectivity radius at an arbitrary point ; How the shortest geodesic point passing through a point looks? etc.. Can Somebody suggest a good reference?

Thanks in advance.

share|improve this question

1 Answer 1

up vote 1 down vote accepted

Alan Beardon's "Geometry of Discrete Groups" should give you all the tools you need to answer your questions (the tools being computation of distances and angles in a convenient model).

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.