Tchebychev nets on spheres
Author:
Sandra Lee Samelson
Journal:
Quart. Appl. Math. 49 (1991), 11-18
MSC:
Primary 53A15
DOI:
https://doi.org/10.1090/qam/1096228
MathSciNet review:
MR1096228
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Abstract: We show that the standard sphere on $\mathbb {R}{^3}$ admits a Tchebychev net which covers an open subset of the sphere which contains a closed hemisphere.
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P. L Tchebychev, Sur la coupe des vêtements, Assoc. franç. pour l’avancement des sci., Congrés de Paris, 154–155 (1878)
L. Bieberbach, Über Tchebychefsche Netz auf Flächen negative Krümmung, S-b Preuss. Akad. Wiss., Phys. Math. Kl. 23, 294–321 (1926)
J. N. Hazzidakis, Über einige Eigenschaften der Flächen mit constantem Krümmungsmass, J. Reine und Angew. Math. (Crelle’s J.) 88, 68–73 (1880)
W. Klingenberg, Riemannian geometry, Lectures on Closed Geodesics, Springer-Verlag, Berlin-Heidelberg-New York, 1978
A. C. Pipkin, Equilibrium of Tchebychev nets, Arch. Rational Mech. Anal. 1, 81–97 (1984)
M. Servant, Sur l’habillage des surfaces, C. R. Acad. Sci. 137, 112–115 (1903)
S. Samelson, Generalized Tchebychev nets, M. Sc. Thesis, Department of Mathematics, Carnegie Mellon University, 1986
J. J. Stoker, Differential Geometry, Wiley, New York, 1969
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Article copyright:
© Copyright 1991
American Mathematical Society