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General helices and a Theorem of Lancret


Author: Manuel Barros
Journal: Proc. Amer. Math. Soc. 125 (1997), 1503-1509
MSC (1991): Primary 53C40, 53A05
DOI: https://doi.org/10.1090/S0002-9939-97-03692-7
MathSciNet review: 1363411
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Abstract: We present a theorem of Lancret for general helices in a 3-dimen-
sional real-space-form which gives a relevant difference between hyperbolic and spherical geometries. Then we study two classical problems for general helices in the 3-sphere: the problem of solving natural equations and the closed curve problem.


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Additional Information

Manuel Barros
Affiliation: Departamento de Geometria y Topologia, Facultad de Ciencias, Universidade de Granada, 18071 Granada, Spain
Email: mbarros@goliat.ugr.es

DOI: https://doi.org/10.1090/S0002-9939-97-03692-7
Keywords: General helix, theorem of Lancret, Hopf cylinder
Received by editor(s): July 26, 1995
Received by editor(s) in revised form: November 14, 1995
Additional Notes: Partially supported by DGICYT Grant No. PB94-0750.
Communicated by: Christopher Croke
Article copyright: © Copyright 1997 American Mathematical Society

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