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Licensed Unlicensed Requires Authentication Published by De Gruyter May 17, 2006

Variational character of the Cauchy-Riemann equations

  • R. Ferreiro Pérez EMAIL logo and J. Muñoz Masqué
From the journal


Cauchy-Riemann equations for smooth maps ϕ: ℂ → ℂk are proved to be of variational type if and only if k is even. This fact is seen to be related to a complex differential form of degree (3, 0) on ℂ × ℂk, which exists only for an even k. The Lie algebra of infinitesimal symmetries of the Hamiltonian structure associated with Cauchy-Riemann equations is also determined.


Permanent address: Instituto de Física Aplicada, CSIC, 28006-Madrid, Spain.

(Communicated by Héctor J. Sussmann)

Received: 2004-08-27
Published Online: 2006-05-17
Published in Print: 2006-03-21

© Walter de Gruyter

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