Results in Mathematics

, Volume 4, Issue 1–2, pp 128–140 | Cite as

A variational proof of the Allendoerfer-Weil formula including a covering theorem for differentiable manifolds

  • Moritz Armsen
Forschungsbeiträge Research paper


Riemannian Metrics Christoffel Symbol Finite Family Codazzi Equation Closed Hypersurface 
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]
    C.B. Allendoerfer and A. Weil, The Gauss-Bonnet theorem for Riemannian polyhedra. Trans. Amer. Math. Soc. 53 (1943), 101–129.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    M. Armsen, A variational proof of the Gauss-Bonnet formula. Manuscripta Math. 20 (1977), 245–253.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    D. Lovelock, The Einstein tensor and its generalizations. J. Math. Phys. 12 (1971), 498–501.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    J. R. Munkres, Elementary differential topology. Annals of Math. Studies, No. 54, Princeton University Press, Princeton, 1966.Google Scholar
  5. [5]
    H. Rund, Variational problems involving combined tensor fields. Abh. Math. Sem. Univ. Hamburg 29 (1966), 243–262.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    H. Rund, Invariant theory of variational problems on subspaces of a Riemannian manifold. Hamburger Math. Einzelschriften, Neue Folge, Heft 5, Vandenhoeck & Ruprecht, Göttingen, 1971.Google Scholar
  7. [7]
    H. Whitney, Geometric integration theory. Princeton University Press, Princeton, 1957.CrossRefMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1981

Authors and Affiliations

  • Moritz Armsen
    • 1
  1. 1.Abteilung Mathematik der Universität DortmundDortmund 50

Personalised recommendations