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Conformal immersions of compact Riemann surfaces into the 2n-sphere (n ≥ 2)

Published online by Cambridge University Press:  22 January 2016

Jun-Ichi Hano
Jun-Ichi Hano*
Affiliation:
Washington University, (jihano@artsci.wustl.edu)
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The purpose of this article is to prove the following theorem:

Let n be a positive integer larger than or equal to 2, and let S be the unit sphere in the 2n + 1 dimensional Euclidean space. Given a compact Riemann surface, we can always find a conformal and minimal immersion of the surface into S whose image is not lying in any 2n — 1 dimensional hyperplane.

This is a partial generalization of the result by R. L. Bryant. In this papers, he demonstrates the existence of a conformal and minimal immersion of a compact Riemann surface into S2n, which is generically 1:1, when n = 2 ([2]) and n = 3 ([1]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 141 , March 1996 , pp. 79 - 105
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

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