Inventiones mathematicae

, Volume 59, Issue 2, pp 119–143 | Cite as

Geodesics on the ellipsoid

  • Horst Knörrer


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  1. 1.
    Arnold, V.I.: Mathematical Methods of Classical Mechanics. Berlin-Heidelberg-New York: Springer-Verlag 1978Google Scholar
  2. 2.
    Chasles, M.: Les lignes géodésiques et les lignes de courbure des surfaces du second degré. Journ. de Math.11, 5–20 (1846)Google Scholar
  3. 3.
    Desale, D.V., Ramanan, S.: Classification of vector bundles of rank 2 on hyperelliptic curves. Inv. math.38, 161–186 (1977)Google Scholar
  4. 4.
    Donagi, R.: Group law on intersections of two quadrics. Preprint UCLA 1978Google Scholar
  5. 5.
    Griffiths, P., Harris, J.: Principles of Algebraic Geometry. New York: John Wiley 1978Google Scholar
  6. 6.
    Hilbert, D., Cohn-Vossen, S.: Anschauliche Geometrie. Berlin-Heidelberg-New York: Springer Verlag 1932Google Scholar
  7. 7.
    Hodge, W., Pedoe, D.: Methods of Algebraic Geometry. Cambridge University Press 1952Google Scholar
  8. 8.
    Jacobi, C.: Vorlesungen über Dynamik. Gesammelte Werke, Supplementband, Berlin 1884Google Scholar
  9. 9.
    Klingenberg, W.: Paare symmetrischer und alternierender Formen zweiten Grades. Abh. Math. Seminar Hamburg19, 78–93 (1955)Google Scholar
  10. 10.
    Moser, J.: Various Aspects of integrable Hamiltonian systems. To appear in Proceedings of the CIME Conference held in Bressanone, Italy, June 1978Google Scholar
  11. 11.
    Moser, J.: Geometry of quadrics and spectral theory. Lecture delivered at a symposium in honour of S.S. Chern, Berkeley 1979Google Scholar
  12. 12.
    Mumford, D.: Curves and their Jacobians. The University of Michigan Press 1975Google Scholar
  13. 13.
    Mumford, D.: An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg De Vries equation and related non-linear equations, pp. 115–153. Proc. Intern. Symp. on Algebraic Geometry, Kyoto 1977Google Scholar
  14. 14.
    Rauch, H., Farkas, H.: Theta Functions with Applications to Riemann Surfaces. Baltimore: Williams & Wilkins 1974Google Scholar
  15. 15.
    Reid, M.: The complete intersection fo two or more quadrics. Thesis, Cambridge (GB) 1972Google Scholar
  16. 16.
    Salmon, G.: A Treatise on the Analytic Theory of Three Dimensions. Seventh Edition 1927 Chelsea, New YorkGoogle Scholar
  17. 17.
    Staude, O.: Geometrische Deutung der Additionstheoreme der hyperelliptischen Integrale und Funktionen erster Ordnung im System der confocalen Flächen 2. Grades. Math. Ann.82, 1–69 und 145–176 (1883)Google Scholar
  18. 18.
    Tyurin, A.N.: On intersections of quadrics. Russian Math. Surveys30, 51–105 (1975)Google Scholar
  19. 19.
    Weierstrass, K.: Über die geodätischen Linien auf dem dreiachsigen Ellipsoid. Math. WerkeI, 257–266Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Horst Knörrer
    • 1
  1. 1.Mathematisches InstitutUniversität BonnBonnGermany

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