Journal of the Mathematical Society of Japan

Thread construction revisited

Jin-ichi ITOH and Kazuyoshi KIYOHARA

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Staude's thread construction of ellipsoid is revisited from a new view-point concerning the length of geodesic segments. Thanks to the general nature of this view-point, one obtains similar thread construction on other stages, i.e., on “Liouville manifolds”.

Article information

Source
J. Math. Soc. Japan Volume 68, Number 3 (2016), 917-938.

Dates
First available in Project Euclid: 19 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1468956152

Digital Object Identifier
doi:10.2969/jmsj/06830917

Mathematical Reviews number (MathSciNet)
MR3523531

Zentralblatt MATH identifier
1353.53048

Subjects
Primary: 53C22: Geodesics [See also 58E10]
Secondary: 53A05: Surfaces in Euclidean space

Keywords
ellipsoid thread construction Liouville manifold geodesic

Citation

ITOH, Jin-ichi; KIYOHARA, Kazuyoshi. Thread construction revisited. J. Math. Soc. Japan 68 (2016), no. 3, 917--938. doi:10.2969/jmsj/06830917. https://projecteuclid.org/euclid.jmsj/1468956152.


Export citation

References

  • I. Dinca, Thread configurations for ellipsoids, preprint, arXive:0902.1421v1 [math.DG].
  • D. Hilbert and S. Cohn-Vossen, Geometry and the imagination, Chelsea, New York, 1952 (translation from “Anshauliche Geometrie”, Springer, Berlin, 1932).
  • J. Itoh and K. Kiyohara, The cut loci and the conjugate loci on ellipsoids, Manuscripta Math., 114 (2004), 247–264.
  • J. Itoh and K. Kiyohara, The cut loci on ellipsoids and certain Liouville manifolds, Asian J. Math., 14 (2010), 257–290.
  • J. Itoh and K. Kiyohara, Cut loci and conjugate loci on Liouville surfaces, Manuscripta Math., 136 (2011), 115–141.
  • K. Kiyohara, Two classes of Riemannian manifolds whose geodesic flows are integrable, Mem. Amer. Math. Soc., 130/619 (1997).
  • Laboratorio di Macchine Matematiche (web site), http://www.museo.unimo.it/theatrum/macchine/lab_sez1.htm
  • F. van Schooten, De organica conicarum sectionum constructione, Lione, Elsevier, 1646.
  • O. Staude, Ueber Fadenconstructionen des Ellipsoides, Math. Ann., 20 (1882), 147–184.