Uniqueness of the stereographic embedding

Michael Eastwood

Archivum Mathematicum (2014)

  • Volume: 050, Issue: 5, page 265-271
  • ISSN: 0044-8753

Abstract

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The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.

How to cite

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Eastwood, Michael. "Uniqueness of the stereographic embedding." Archivum Mathematicum 050.5 (2014): 265-271. <http://eudml.org/doc/262198>.

@article{Eastwood2014,
abstract = {The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.},
author = {Eastwood, Michael},
journal = {Archivum Mathematicum},
keywords = {stereographic; conformal circles; compactification; stereographic projection; conformal circles; compactification},
language = {eng},
number = {5},
pages = {265-271},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Uniqueness of the stereographic embedding},
url = {http://eudml.org/doc/262198},
volume = {050},
year = {2014},
}

TY - JOUR
AU - Eastwood, Michael
TI - Uniqueness of the stereographic embedding
JO - Archivum Mathematicum
PY - 2014
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 050
IS - 5
SP - 265
EP - 271
AB - The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.
LA - eng
KW - stereographic; conformal circles; compactification; stereographic projection; conformal circles; compactification
UR - http://eudml.org/doc/262198
ER -

References

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  1. Bailey, T.N., Eastwood, M.G., 10.1090/S0002-9939-1990-0994771-7, Proc. Amer. Math. Soc. 108 (1990), 215–221. (1990) Zbl0684.53016MR0994771DOI10.1090/S0002-9939-1990-0994771-7
  2. Cartan, É., Les espaces à connexion conforme, Ann. Soc. Polon. Math. (1923), 171–221. (1923) 
  3. Francès, C., Rigidity at the boundary for conformal structures and other Cartan geometries, arXiv:0806:1008. 
  4. Francès, C., Sur le groupe d’automorphismes des géométries paraboliques de rang 1, Ann. Sci. École Norm. Sup. 40 (2007), 741–764. (2007) Zbl1135.53016MR2382860
  5. The Maple program: http://www.maplesoft.com, ple program: http://www.maplesoft.com. 
  6. Tod, K.P., 10.1016/j.geomphys.2012.03.010, J. Geom. Phys. 62 (2012), 1778–1792. (2012) Zbl1245.53042MR2925827DOI10.1016/j.geomphys.2012.03.010
  7. Yano, K., The Theory of Lie Derivatives and its Applications, North-Holland 1957. Zbl0077.15802MR0088769

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