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A characterisation of Helices and Cornu spirals in real space forms

Published online by Cambridge University Press:  17 April 2009

J. Arroyo
Affiliation:
Departamento de Geometris y TopologiaUniversidad de Granada18071 GranadaSpain e-mail: mbarros@goliat.ugr.es
M. Barros
Affiliation:
Departamento de MatématicasFacultad de CienciasUniversidad del Pail Vasco/Euskal Herriko Unibertsitatea48080 BilbaoSpain e-mail: mtpgabeo@lg.ehu.es
O.J. Garay
Affiliation:
Departamento de MatématicasFacultad de CienciasUniversidad del Pail Vasco/Euskal Herriko Unibertsitatea48080 BilbaoSpain e-mail: mtpgabeo@lg.ehu.es
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Abstract

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We classify unit speed curves contained in a real space form of arbitrary dimension Nm(c), whose mean curvature vector is proper for the Laplacian. Then we use these results to classify Hopf cylinders of S3 and semi-Riemannian Hopf cylinders of with proper mean curvature function.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

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