Projective differential geometry of multidimensional dispersionless integrable hierarchies
Abstract
We introduce a general setting for multidimensional dispersionless integrable hierarchy in terms of differential mform Ω_{m} with the coefficients satisfying the Plücker relations, which is gaugeinvariantly closed and its gaugeinvariant 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 gaugeinvariant closedness equations.
 Publication:

Journal of Physics Conference Series
 Pub Date:
 March 2014
 DOI:
 10.1088/17426596/482/1/012005
 arXiv:
 arXiv:1310.0203
 Bibcode:
 2014JPhCS.482a2005B
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 Mathematics  Differential Geometry
 EPrint:
 10 pages, the text of the talk at PMNP2013 (Gallipoli, Italy, 2229 June 2013)