Skip to main content
SpringerLink
Log in

Eigenvalue equations in curve theory

Part I: Characterizations of Conic Sections

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

We characterize conic sections in the Euclidean plane in terms of appropriate eigenfunctions of second order on their spherical image; we clarify the affine background of such results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S.S. Chern, C.L. Terng: An analogue of Baeeklund’s Theorem in Affine Geometry, Rocky Mountain Journal of Mathematics 10, 105–124 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  2. W. Blaschke: Vorlesungen über Differentialgeometrie, Vol II, Springer Verlag, Berlin 1923.

    Google Scholar 

  3. J. Leder, A. Schwenk-Schellschmidt, U. Simon, and M. Wiehe: Generating higher order Codazzi tensors by functions, Geometry and Topology of Submanifolds IX (1999), World Sci., Singapore, 174–191.

    Chapter  Google Scholar 

  4. R. Schneider: Zur affinen Differentialgeometrie im Gro\en I. Math. Z. 101, 375–406 (1967)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FB II Mathematik-Physik-Chemie, TFH Berlin, Luxemburger Str. 10, D-13353, Berlin

    A. Schwenk-Schellschmidt

  2. Institut für Mathematik, TU Berlin, MA 8-3, Straβe des 17. Juni 135, D-10623, Berlin

    U. Simon & M. Wiehe

Authors
  1. A. Schwenk-Schellschmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. U. Simon
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Wiehe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Schwenk-Schellschmidt.

Additional information

Dedicated to S.S. Chern

Research partially supported by DFG Si-163/7-2

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schwenk-Schellschmidt, A., Simon, U. & Wiehe, M. Eigenvalue equations in curve theory. Results. Math. 40, 273–285 (2001). https://doi.org/10.1007/BF03322712

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322712

MSC 2000

Keywords

Search

Navigation