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From almost (para)-complex structures to affine structures on Lie groups
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 ...
Generalized geometric structures on complex and symplectic manifolds
(Springer Heidelberg, 2015-10)
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 ...
Interpolation of geometric structures compatible with a pseudo Riemannian metric
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 ...