Discriminants of convex curves

are homeomorphic

Author:
B. Shapiro

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1923-1930

MSC (1991):
Primary 14H50

DOI:
https://doi.org/10.1090/S0002-9939-98-04766-2

MathSciNet review:
1487339

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Abstract | References | Similar Articles | Additional Information

Abstract: For a given real generic curve let denote the ruled hypersurface in consisting of all osculating subspaces to of codimension 2. In this note we show that for any two convex real projective curves and the pairs and are homeomorphic.

**[Ar1]**V. I. Arnold,*On the number of flattening points on space curves*, preprint of the Mittag-Leffler Institute (1) (1994/95), 1-13, Sinai's Moscow seminar on Dynamical Systems, AMS Transl., Ser. 2, vol. 171, 1995, pp. 11-22. MR**96i:53070****[Ar2]**V. I. Arnold,*Topological problems in the theory of wave propagation*, Russian Math. Surveys**51**(1) (1996), 1-49. MR**97c:58001****[Co]**W. A. Coppel,*Discojugacy*, Lecture Notes in Math., vol. 220, Springer-Verlag, 1971. MR**57:778****[Ish]**G. Ishikawa,*Developable of a curve and determinacy relative to osculating type*, Quart. J. Math., Oxford Ser (2)**46**(184) (1995), 437-451. CMP**96:06****[Sh1]**B. Shapiro,*Space of linear differential equations and flag manifolds*, Math. USSR - Izv.**36**(1) (1990), 183-197. MR**91g:58030****[Sh2]**B. Shapiro,*Towards qualitative theory for high order linear ODE*, in preparation.**[ShS]**B. Shapiro and V. Sedykh,*On Young hulls of convex curve in*, preprint MPI 96-95.**[MSh]**M. Shapiro,*Topology of the space of nondegenerate curves*, Math. USSR - Izv.**57**(1993), 106-126. MR**94k:58019**

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Additional Information

**B. Shapiro**

Affiliation:
Department of Mathematics, University of Stockholm, S-10691, Sweden

Email:
shapiro@matematik.su.se

DOI:
https://doi.org/10.1090/S0002-9939-98-04766-2

Keywords:
Convex curves,
discriminants

Received by editor(s):
December 17, 1996

Communicated by:
Christopher Croke

Article copyright:
© Copyright 1998
American Mathematical Society