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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$C^ \infty$-invariants on loop spaces
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by Wing Sum Cheung PDF
Proc. Amer. Math. Soc. 100 (1987), 322-328 Request permission

Abstract:

We compute all the ${C^\infty }$-invariants on the spaces of immersions $C_I^\infty ({S^1},S)$ and $C_I^\infty ({S^1},{{\mathbf {R}}^3})$, where $S$ is a surface of constant curvature, by using Griffiths’ formalism on the calculus of variations via exterior differential systems.
References
    R. Bryant, S. S. Chern, and P. Griffiths, Exterior differential systems, Proc. Beijing Sympos. on Differential Geometry and Differential Equations, 1980. E. Cartan, Les systÚmes différentielles extérieurs et leurs applications géométriques, Hermann, Paris, 1945.
  • A. P. Stone, Higher order conservation laws, J. Differential Geometry 3 (1969), 447–456. MR 264536, DOI 10.4310/jdg/1214429064
  • Phillip A. Griffiths, Exterior differential systems and the calculus of variations, Progress in Mathematics, vol. 25, BirkhĂ€user, Boston, Mass., 1983. MR 684663
  • Shlomo Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0193578
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 100 (1987), 322-328
  • MSC: Primary 58D10; Secondary 53C20, 57R42, 58E10
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0884473-X
  • MathSciNet review: 884473