Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



On Darboux's lemma

Author: Hans Samelson
Journal: Proc. Amer. Math. Soc. 70 (1978), 126-128
MSC: Primary 58A10
MathSciNet review: 0474367
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We resurrect Carathéodory's proof of Darboux's lemma (normal form $ \Sigma d{p_i}d{q_i}$ for a nondegenerate closed 2-form). The proof is simple and straightforward (after eliminating unnecessary steps) and deserves to be better known. It involves, not surprisingly, the canonical differential equations of Hamilton-Jacobi theory.

References [Enhancements On Off] (What's this?)

  • [1] C. Carathéodory, Variationsrechnung und partielle Differentialgleichungen erster Ordnung, Teubner, Leipzig, 1935; English edition: Calculus of variations and partial differential equations of first order, Holden-Day, San Francisco, 1965.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58A10

Retrieve articles in all journals with MSC: 58A10

Additional Information

Article copyright: © Copyright 1978 American Mathematical Society