10
$\begingroup$

I am looking for an introductory textbook to the geometry of the hyperbolic space $\mathbb{H}^n$. The book should include explicit description of geodesics and horospheres in various models (hyperboloid, Poincaré, Klein).

Apologies if the question is not appropriate for this site.

$\endgroup$
7
$\begingroup$

I really like Ratcliffe’s account of the 3 models ($H^n$, $U^n$, $B^n$) in Foundations of Hyperbolic Manifolds (2006, Chap. 3–5). It has what you ask for, and also copious exercises and historical notes.

$\endgroup$
  • $\begingroup$ I second this. It's a large book, but I remember it being very readable. $\endgroup$ – Greg Friedman 2 days ago
6
$\begingroup$

W. Thurston, Three-dimensional geometry and topology.

$\endgroup$
2
$\begingroup$

Prasolov, V. V.; Tikhomirov, V. M., Geometry. Transl. from the Russian by O. V. Sipacheva. Transl. edited by A. B. Sossinski, Translations of Mathematical Monographs. 200. Providence, RI: American Mathematical Society (AMS). xi, 257 p. (2001). ZBL0977.51001.

$\endgroup$
1
$\begingroup$

You might try the following:

  1. Jürgen Richter-Gebert: Perspectives on Projective Geometry,
  2. David Mumford, Caroline Series, David Wright: Indra´s Pearls.
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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