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Space forms: a history

Klaus Volkert


This article presents the history of space forms beginning with Clifford’s flat torus (1873) and ending with Hopf’s paper (1925) and related work by Seifert, Threlfall, Hantzsche and Wendt. In particular we study the work on space forms done by Killing (1876 – 1893).


space form, history of topology

Mathematical Subject Classification 2010

Primary: 01A55, 01A60


Received: 11th November 2012
Accepted: 12th February 2013
Published: 13th May 2013
Editor: Erhard Scholz