Functional Analysis and Its Applications

, Volume 32, Issue 2, pp 75–80 | Cite as

Towards the legendre sturm theory of space curves

  • V. I. Arnold


Projective Space Generic Curve Original Curve Space Curf Morse Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    O. P. Shcherbak, “Projectively dual space curves and Legendre singularities,” Proc. Tbilisi Univ.,232/233, 280–336 (1982); English transl. in Selecta Math. Sov.,5, No. 4, 391–421 (1986).MathSciNetGoogle Scholar
  2. 2.
    V. I. Arnold, “Wave front evolution and equivariant Morse lemma,” Commun. Pure Appl. Math.,29, No. 6, 557–582 (1976).zbMATHGoogle Scholar
  3. 3.
    V. I. Arnold, “On the number of flattening points on space curves,” in: Ya. G. Sinai's Moscow Seminar on Dynamical Systems, Am. Math. Soc. Transl., Ser. 2, Vol. 171, Providence, 1995, pp. 11–22.Google Scholar
  4. 4.
    M. Barner, “Über die Mindestanzahl stationären Schmeigebenen bei geschlossenen streng konvexen Raumkurven,” Abh. Math. Sem. Univ. Hamburg,20, 196–215 (1956).zbMATHMathSciNetGoogle Scholar
  5. 5.
    V. Arnold, Singularities of Caustics and Wave Fronts, Kluwer, Dordrecht, 1990 (§5.2, p. 100).zbMATHGoogle Scholar
  6. 6.
    J. J. Nuňo Ballesteros and M. C. Romero Fuster, “Global bitangency properties of generic closed space curves,” Math. Proc. Cambridge Philos. Soc.,112, 519–526 (1992).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    V. A. Vassiliev, “Self-intersections of wavefronts and Legendre (Lagrangian) characteristic numbers,” Funkts. Anal. Prilozhen.,16, No. 2, 68–69 (1982); English transl. in Funct. Anal. Appl.,16, No. 2, 131–133 (1982).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. I. Arnold

There are no affiliations available

Personalised recommendations