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The Carathéodory limiting spherical shells in the euclidean hypersphere

Published online by Cambridge University Press:  26 February 2010

A. A. Fadlalla
A. A. Fadlalla
Affiliation:
Faculty of Science, Cario University, Giza, Egypt.
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Extract

By means of all functions regular in a domain †G ⋐ Cn Carathéodory [1,2] defined a metric in G. As usual, using this metric, we can define spherical shells in G. That is, if DG(t, q) denotes the Carathéodory metric between t, q∈G measured in G, then the Caratheéodory spherical shell S(t, q) passing through q and with centre t is defined by:

Type
Research Article
Information
Mathematika , Volume 13 , Issue 1 , June 1966 , pp. 69 - 75
Copyright
Copyright © University College London 1966

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References

1. Carathéodory, C., Conformal representation (Cambridge Math. Tract, 1932)Google Scholar
2. Carathéodory, C., “Über das Sehwarzsohe Lemma bei analytischen funktionen von zwei komplexen veränderlichen”, Math. Annalen, 97 (1927).CrossRefGoogle Scholar
3. Sommer, F., Die geometrie der hyperkugelautomorphismen. Schriftenreihe des Math.Instituts der universitäat Münster, Heft 3 (Münster, 1949).Google Scholar