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The equi-affine and Frenet curvatures of curves in pseudo-Riemannian 2-manifolds

Volume 150 / 2017

Karina Olszak, Zbigniew Olszak Colloquium Mathematicum 150 (2017), 103-112 MSC: Primary 53C42; Secondary 53B05, 53B30, 53C50. DOI: 10.4064/cm7167s-3-2017 Published online: 24 August 2017

Abstract

For an arbitrary nondegenerate curve in a pseudo-Riemannian (including Riemannian) 2-manifold, we express the equi-affine curvature with the help of the Frenet (geodesic) curvature of this curve.

Authors

  • Karina OlszakDepartment of Mathematics
    Wrocław University of Science
    and Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Zbigniew OlszakDepartment of Applied Mathematics
    Wrocław University of Science
    and Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

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