Results in Mathematics

, Volume 50, Issue 1–2, pp 109–124 | Cite as

Eigenvalue Equations in Curve Theory Part II: Evolutes and Involutes

  • Stephanie Müller
  • Angela Schwenk-Schellschmidt
  • Udo Simon


We study plane Euclidean curves with positive curvature κ and spherical parametrization s.t. their radius of curvature κ−1 satisfies an eigenvalue equation. We investigate this class in detail in terms of evolutes and involutes and their geometric properties in relation to the eigenvalue equations considered. For a curve c in this class, the radius of curvature of its evolute satisfies the same eigenvalue equation like κ−1 of c, while the radii of curvature of its involutes satisfy a slightly modified eigenvalue equation. We give a complete local classification of all types of curves in this class.

Mathematics Subject Classification (2000).

53A04 34A30 34L15 53A17 


Euclidean plane curves curvature function support function evolutes involutes eigenvalue equations 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Stephanie Müller
    • 1
  • Angela Schwenk-Schellschmidt
    • 2
  • Udo Simon
    • 3
  1. 1.BerlinGermany
  2. 2.TFH BerlinBerlinGermany
  3. 3.Institut f. Mathematik MA 8-3TU BerlinBerlinGermany

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