O ct 2 00 0 Families of ( 1 , 2 ) – Symplectic Metrics on Full Flag Manifolds ∗

Families of (1,2)-symplectic Metrics on Full Flag Manifolds

ar X iv : 0 80 4 . 18 38 v 2 [ m at h . D G ] 4 A ug 2 00 8 AHS – STRUCTURES AND AFFINE HOLONOMIES

We show that a large class of non–metric, non–symplectic affine holonomies can be realized, uniformly and without case by case considerations, by Weyl connections associated to the natural AHS–structures on certain generalized flag manifolds.

ar X iv : 0 71 0 . 44 41 v 1 [ m at h . D G ] 2 4 O ct 2 00 7 Calabi - Yau cones from contact reduction

We consider a generalization of Sasaki-Einstein manifolds, which we characterize in terms both of spinors and differential forms, that in the real analytic case corresponds to contact manifolds whose symplectic cone is Calabi-Yau. We construct solvable examples in seven dimensions. Then, we consider circle actions that preserve the structure, and determine conditions for the contact reduction t...

A pr 2 00 1 Geometry of Four - vector Fields on

The purpose of this paper if to describe a natural 4-vector field on the quaternionic flag manifolds, which geometrically determines the Bruhat cell decomposition. This structure naturally descends from the symplectic group, where it is related to the dressing action defined via the Iwasawa decomposition of the general linear group over the quaternions.

ar X iv : m at h . SG / 0 40 72 21 v 2 2 1 O ct 2 00 4 Spaces of maps with symplectic graph

We consider the homotopy type of the space Mσ(Σ, Γ) of maps between symplectic surfaces (Σ, σΣ) and (Γ, σΓ) whose graphs form symplectic submanifolds of the product. We give a purely topological model for this space in terms of maps with constrained numbers of pre-images. We use this to show that the dependence of the homotopy type on the forms σΣ and σΓ is quantizedit changes only when the par...