Ptolemy spaces with strong inversions
HTML articles powered by AMS MathViewer
- by
A. Smirnov
Translated by: the author - St. Petersburg Math. J. 25 (2014), 1021-1030
- DOI: https://doi.org/10.1090/S1061-0022-2014-01327-1
- Published electronically: September 8, 2014
- PDF | Request permission
Abstract:
It is proved that a compact Ptolemy space with many strong inversions that contains a Ptolemy circle is Möbius equivalent to an extended Euclidean space.References
- S. Buyalo and V. Schroeder, Moebius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces, arXiv:1012.1699.
- —, Moebius characterization of the boundary at infinity of rank one symmetric spaces, arXiv:1211.3237.
- Thomas Foertsch and Viktor Schroeder, Metric Möbius geometry and a characterization of spheres, Manuscripta Math. 140 (2013), no. 3-4, 613–620. MR 3019142, DOI 10.1007/s00229-012-0555-0
- I. J. Schoenberg, A remark on M. M. Day’s characterization of inner-product spaces and a conjecture of L. M. Blumenthal, Proc. Amer. Math. Soc. 3 (1952), 961–964. MR 52035, DOI 10.1090/S0002-9939-1952-0052035-9
Bibliographic Information
- A. Smirnov
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, Saint Petersburg 191023, Russia
- ORCID: 0000-0002-6781-2105
- Email: alvismi@gmail.com
- Received by editor(s): January 23, 2013
- Published electronically: September 8, 2014
- Additional Notes: Supported by RFBR (grant no. 11-01-00302-a).
- © Copyright 2014 American Mathematical Society
- Journal: St. Petersburg Math. J. 25 (2014), 1021-1030
- MSC (2010): Primary 53C70
- DOI: https://doi.org/10.1090/S1061-0022-2014-01327-1
- MathSciNet review: 3234843