We introduce a notion of compatibility between (almost) Dirac structures and (1,1)-tensor fields extending that Poisson-Nijenhuis structures. study several properties the "Dirac-Nijenhuis" thus obtained, including their connection with holomorphic structures, geometry leaves quotients, as well presence hierarchies. also consider integration to Lie groupoids, which includes special case.

A field of endomorphisms R is called a Nijenhuis operator if its torsion vanishes. In this work we study specific kind singular points scalar type. We show that the tangent space at such possesses natural structure left-symmetric algebra (also known as pre-Lie or Vinberg-Kozul algebras). Following Weinstein's approach to linearization Poisson structures, state linearisation problem for operator...

We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skewsymmetric Nijenhuis tensor. We investigate up to what extent the Nijenhuis tensor fails to be parallel with respect to the characteristic connexion. This is naturally described by means of an extension of the notion of Killi...

In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this formulation and show that they are essentially a basis of the cotangent bundle to the tangent bundle to phase-space. In this space we introduce an extended Poisson brackets st...

We find a new class of (2,0)-supersymmetric two-dimensional sigma models with torsion and target spaces almost complex manifolds extending similar results for models with (2,2) supersymmetry. These models are invariant under a new symmetry which is generated by a Noether charge of Lorentz weight one and it is associated to the Nijenhuis tensor of the almost complex structure of the sigma model ...

Talk at the “Pacific Conference on Gravitation and Cosmology”, 1-6 February 1996, Seoul, Korea The second Noether theorem [1] and Dirac-Bergmann constraint theory [2,3] are the basis respectively of the Lagrangian and Hamiltonian formulations of all relativistic physical systems [4]. The need of redundant variables, to be reduced due to the presence of either first and/or second class constrain...

The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton–Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis integrability conditions. The latter are a system of three non-linear partial differential equations. We give a simple and completely algebraic proof that for...