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Geodesic Groups of Minimal Surfaces

Published online by Cambridge University Press:  20 November 2018

H. G. Helfenstein
H. G. Helfenstein*
Affiliation:
University of Alberta
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In a previous paper (6) we have studied those minimal surfaces which admit geodesic mappings without isometries or similarities on another, not necessarily minimal, surface. Here we determine all pairs of minimal surfaces which can be geodesically mapped on each other. We find that two such surfaces are either:

(i) similar Bonnet associates of each other, or

(ii) both Poisson surfaces (that is, isometric to a plane), or

(iii) both Scherk surfaces (2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 89 - 96
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Bieberbach, L., Lehrbuch der Funktionentheorie, 2, (Berlin, 1931).Google Scholar
2. Blaschke, W., Einfährung in die Differentialgeometrie (Berlin, 1950).Google Scholar
3. Burnside, W., Theory of Groups of Finite Order, (Cambridge, 1911).Google Scholar
4. Coxeter, H. S. M., The abstract groups G m,n,p , Trans. Amer. Math. Soc, 45 (1939), 73-150.Google Scholar
5 Coxeter, H. S. M. f Self-dual configurations and regular graphs, Bull. Amer. Math. Soc, 56 (1950), 413-455.Google Scholar
6. Helfenstein, H. and Wyman, M., Geodesic mapping of minimal surfaces, Math. Annalen, 132 (1956), 310-327.Google Scholar
7. Sinigallia, L., Sulle superficie ad area minima applicabili su se stesse, Giorn. Mat., 36 (1898), 172.Google Scholar