Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-22T12:30:35.898Z Has data issue: false hasContentIssue false
  • English
  • Français

A Geometrical Theory of Multiple Integral Problems in the Calculus of Variations

Published online by Cambridge University Press:  20 November 2018

H. Rund
H. Rund*
Affiliation:
University of the Witwatersrand, Johannesburg, South Africa
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Xn denote an n-dimensional differentiate manifold referred to local coordinates xi. An m-dimensional subspace Cm (m < n) of Xn can be represented parametrically in the form

1.1

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 639 - 657
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Carathéodory, C., TJber die Variationsrechnung bei mehrfachen Integralen, Acta Sci. Math. Szeged), 4 (1929), 193–216.Google Scholar
2. Cartan, E., Les espaces métriques fondés sur la notion d'aire, Actualités scientifiques, 72 Hermann, Paris, 1933).Google Scholar
3. Davies, E. T., A real spaces, Ann. Mat. Pura Appl. (4), 55 (1961), 63–76.Google Scholar
4. Douglas, J., Systems of K-dimensional manifolds in N-dimensional space, Math. Ann., 105 (1931), 707–733.Google Scholar
5. Kawaguchi, A., Theory ofareal spaces, Mat. e Rend. Appl. (5), 12 (1953), 373–386.Google Scholar
6. Martin, D. H., The local geometry and extremal surfaces of areal spaces, Ph.D. thesis, University of South Africa (Pretoria, 1965).Google Scholar
7. Rund, H., The differential geometry of Finsler spaces (Springer, Berlin-Gôttingen-Heidelberg, 1959).10.1007/978-3-642-51610-8CrossRefGoogle Scholar
8. Rund, H., The Hamilton-Jacobi theory in the calculus of variations (Van Nostrand, London and New York, 1966).Google Scholar
9. Weyl, H., Observations on Hilberfs independence theorem and Bom's quantization of field equations, Phys. Rev. (2), 46 (1934), 505–508.Google Scholar
10. Weyl, H., Geodesic fields in the calculus of variations for multiple integrals, Ann. of Math. (2), 36 (1935), 607–629.Google Scholar