Bulletin of the Australian Mathematical Society

Research Article

A characterisation of Helices and Cornu spirals in real space forms

J. Arroyoa1, M. Barrosa2 and O.J. Garaya3

a1 Departamento de Geometris y Topologia Universidad de Granada 18071 Granada Spain e-mail: mbarros@goliat.ugr.es

a2 Departamento de Matématicas Facultad de Ciencias Universidad del Pail Vasco/Euskal Herriko Unibertsitatea 48080 Bilbao Spain e-mail: mtpgabeo@lg.ehu.es

a3 Departamento de Matématicas Facultad de Ciencias Universidad del Pail Vasco/Euskal Herriko Unibertsitatea 48080 Bilbao Spain e-mail: mtpgabeo@lg.ehu.es

Abstract

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 S0004972700030719_inline1 with proper mean curvature function.

(Received August 01 1996)