Projective differential geometry of multidimensional dispersionless integrable hierarchies

Abstract

We introduce a general setting for multidimensional dispersionless integrable hierarchy in terms of differential $m$-form ${\Omega }_m$ with the coefficients satisfying the Plücker relations, which is gauge-invariantly closed and its gauge-invariant coordinates (ratios of coefficients) are (locally) holomorphic with respect to one of the variables (the spectral variable). We demonstrate that this form defines a hierarchy of dispersionless integrable equations in terms of commuting vector fields locally holomorphic in the spectral variable. The equations of the hierarchy are given by the gauge-invariant closedness equations.

10 pages, the text of the talk at PMNP2013 (Gallipoli, Italy, 22-29 June 2013)

References in corpus (1)

• Coisotropic deformations of associative algebras and dispersionless integrable hierarchies

Cited by in corpus (3)

• New integrable (3+1)-dimensional systems and contact geometry
• Linearly degenerate hierarchies of quasiclassical SDYM type
• Integrability properties of symmetric 4+4-dimensional heavenly type equation