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Types of complete Infinitely sheeted Planes

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa, Nagoya, 466-8555, Japan
*
52 Eguchi, Hinaga, Chita, 478-0041, Japan, nakai@daido-it.ac.jp
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Abstract

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We will answer negatively to the question whether the completeness of infinitely sheeted covering surfaces of the extended complex plane have anything to do with their types being parabolic or hyperbolic. This will be accomplished by giving a one parameter family {W[α]: α ∈ A} of complete infinitely sheeted planes W[α] depending on the parameter set A of sequences α = (an)n>1 of real numbers 0 < an ≤ 1/2 (n ≥ 1) such that W[α] is parabolic for ‘small’ α’s and hyperbolic for ‘large’ α’s.

Keywords

30F2030F2530C2530C35
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 176 , 2004 , pp. 181 - 195
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

References

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