Let G= H⋉ K denote a semidirect product Lie group with Lie algebra g= h⊕ k, where k is an ideal and h is a subalgebra of the same dimension as k. There exist some natural split isomorphisms S with S2= ± Id on g: given any ...

On a product manifold (M, r), we consider four geometric structures compatible with r, e.g. hyper-paracomplex or bi-Lagrangian, and define distinguished generalized complex or paracomplex structures on M, which interpolate ...

On a smooth manifold MM, generalized complex (generalized paracomplex) structures provide a notion of interpolation between complex (paracomplex) and symplectic structures on MM. Given a complex manifold M,j, we define six ...

Let (M, g) be a pseudo Riemannian manifold. We consider four geometric structures on M compatible with g: two almost complex and two almost product structures satisfying additionally certain integrability conditions. For ...