Colloquium

An important question in geometry and analysis is to know when two \(k\)-forms \(f\) and \(g\) are equivalent. The problem is therefore to find a map \(arphi\) such that \[arphi^{\ast} ( g) =f. \] We will mostly discuss the symplectic case \(k=2\) and the case of volume forms \(k=n.\) We will give some results when \(3\leq k\leq n-2,\)  the case \(k=n-1\) will also be considered.
The results have been obtained in collaboration with S. Bandyopadhyay, G. Csato and O. Kneuss and can be found, in part, in the book below.

Csato G., Dacorogna B. et Kneuss O., The pullback equation for differential forms, Birkhaüser, PNLDE Series, New York, 83 (2012).