5
$\begingroup$

Does there exist a survey on the early developments of CAT(k) spaces, with the first motivations and the first problems considered? I looked at Bridson and Haefliger's book On metric spaces of non-positive curvature, and I only found the following references:

  • Rinow, Die innere Geometrie der metrischen Raüme. On the period to 1960. However, the book is written in German.

  • Two papers of Alexandrov, written in Russian.

  • Gromov, Hyperbolic groups. Where the term CAT(k) is coined. However, I did not see historical considerations nor references.

The first point is that I do not read German nor Russian... Anyway, these references are old and necessarily are far from being exhaustive nowadays. Do you know if there exists a good reference on the subject?

Improve this question
$\endgroup$
4
  • 2
    $\begingroup$ I cannot look this up right now, but I think this book may be useful: Burago, Dmitri, Yuri Burago, and Sergei Ivanov. A course in metric geometry. Vol. 33. Providence: American Mathematical Society, 2001. $\endgroup$
    – Joseph O'Rourke
    May 3, 2016 at 13:23
  • $\begingroup$ Burago, Burago and Ivanov is a beautiful book, but I don't think it has much historical information. $\endgroup$
    – Ben McKay
    May 3, 2016 at 19:44
  • $\begingroup$ You can look at Alexandrov, A. D., Selected works. Part I. Selected scientific papers. Translated from the Russian by P. S. V. Naidu. Edited and with a preface by Yu. G. Reshetnyak and S. S. Kutateladze. Classics of Soviet Mathematics, 4. Gordon and Breach Publishers, Amsterdam, 1996. $\endgroup$
    – Mikhail Ostrovskii
    May 8, 2016 at 0:19
  • $\begingroup$ Take a look at various papers and books of Anton Petrunin. $\endgroup$
    – Jarek Kędra
    Jul 13, 2017 at 10:33

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.