The Pullback equation for degenerate forms

Saugata Bandyopadhyay; Bernard Dacorogna; Olivier Kneuss

doi:10.3934/dcds.2010.27.657

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2010, Volume 27, Issue 2: 657-691. Doi: 10.3934/dcds.2010.27.657

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The Pullback equation for degenerate forms

1.
Department of Mathematical Sciences, IISER Kolkata, Mohanpur Campus, PO: BCKV Campus Main Office, Mohanpur - 741252, West Bengal
2.
Section de Mathématiques, Station 8, EPFL, 1015 Lausanne

Received: September 30, 2009

Revised: January 31, 2010

Published: June 2010

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Abstract

We discuss the existence of a diffeomorphism $\varphi:\mathbb{R} ^{n}\rightarrow\mathbb{R}^{n}$ such that

φ^∗ (g) =f,

where $f,g:\mathbb{R}^{n}\rightarrow\Lambda^{k}$ are closed differential forms and $2\leq k\leq n-1.$

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Mathematics Subject Classification: Primary: 35Fxx; Secondary: 58A10.

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