1
$\begingroup$

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.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
2
$\begingroup$

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).

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .