The projective Cartan-Klein geometry of the Helmholtz conditions

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doi:10.3934/jgm.2018003

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2018, Volume 10, Issue 1: 69-92. Doi: 10.3934/jgm.2018003

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The projective Cartan-Klein geometry of the Helmholtz conditions

Setor de Ciências Exatas, Centro Politécnico, Caixa Postal 019081, CEP 81531-990, Curitiba, PR, Brazil

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* Corresponding author

Received: March 31, 2016

Revised: July 31, 2017

Published: February 2018

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Abstract

We show that the Helmholtz conditions characterizing differential equations arising from variational problems can be expressed in terms of invariants of curves in a suitable Grassmann manifold.

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Mathematics Subject Classification: Primary: 49K05; Secondary: 53C35.

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References

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