Integrability conditions for a certain class of nonlinear evolution equations and Kähler geometry

E.M. Isaenko
1991 Differential geometry and its applications  
Isaenko, E.M., Integrability conditions for a certain class of nonlinear evolution equations and Kahler geometry, Diff. Geom. Appl. 1 (1991) 327-344. Abstract: Multicomponent evolution equations associated with linear connections on complex manifolds are considered. It is proved that under some general assumptions an equation from this class is integrable by inverse scattering method iff the corresponding linear connection is the Levi-Civita connection of an indefinite Kahlerian metric of
more » ... nt holomorphic sectional curvature. This result is based on a certain characterization of the above-mentioned Levi-Civita connections. It is shown that the obtained integrable equations are generalized ferromagnetics, and recurrent formulas for their local conservation laws are given.
doi:10.1016/0926-2245(91)90012-x fatcat:5nwczzr5szdldd4uruxq2hz7o4