We consider some differential geometric classes of local and nonlocal Poisson and sym-plectic structures on loop spaces of smooth manifolds which give natural Hamiltonian or multihamiltonian representations for some important nonlinear equations of mathematical physics and field theory such as nonlinear sigma models with torsion, degenerate Lagrangian… (More)
We solve the problem of description for nonsingular pairs of compatible flat metrics in the general N-component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics) are found and integrated. The integrating of these equations is… (More)
On integrability of the equations for nonsingular pairs of compatible flat metrics
Nonlocal Hamiltonian operators of hydrodynamic type with flat metrics, integrable hierarchies and the equations of associativity
Compatible nonlocal Poisson brackets of hydrodynamic type, and integrable hierarchies related to them
Let us consider a function of n independent variables F (t n) satisfying the following two conditions: 1. The matrix η αβ = ∂ 3 F ∂t 1 ∂t α ∂t β is constant and nondegenerate. Note that the matrix η αβ completely determines dependence of the function F on the fixed variable t 1 .
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlin-ear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of potential flat torsionless submanifolds. We show that all potential flat torsionless submanifolds in… (More)
Compatible metrics of constant Riemannian curvature: local geometry, nonlinear equations and integrability