Geodesic
Uniqueness of the stereographic embedding
Archivum mathematicum, Tome 50 (2014) no. 5, pp. 265-271 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2014-5-265
Classification : 53A30, 53C22
Keywords: stereographic; conformal circles; compactification 
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Eastwood, Michael. Uniqueness of the stereographic embedding. Archivum mathematicum, Tome 50 (2014) no. 5, pp. 265-271. doi: 10.5817/AM2014-5-265

[1] Bailey, T.N., Eastwood, M.G.: Conformal circles and parametrizations of curves in conformal manifolds. Proc. Amer. Math. Soc. 108 (1990), 215–221. | DOI | MR | Zbl

[2] Cartan, É.: Les espaces à connexion conforme. Ann. Soc. Polon. Math. (1923), 171–221.

[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. | MR | Zbl

[5] The Maple program: http://www.maplesoft.com</b> ple program: http://www.maplesoft.com

[6] Tod, K.P.: Some examples of the behaviour of conformal geodesics. J. Geom. Phys. 62 (2012), 1778–1792. | DOI | MR | Zbl

[7] Yano, K.: The Theory of Lie Derivatives and its Applications. North-Holland 1957. | MR | Zbl

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