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General helices and a Theorem of Lancret
Author(s):
Manuel
Barros
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1503-1509.
MSC (1991):
Primary 53C40, 53A05
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:
10.1090/S0002-9939-97-03692-7
PII:
S 0002-9939(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
Copyright of article:
Copyright
1997,
American Mathematical Society
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