Lorenz Schwachhöfer

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By a special symplectic connection we mean a torsion free connection which is either the LeviCivita connection of a Bochner-Kähler metric of arbitrary signature, a Bochner-bi-Lagrangian connection, a connection of Ricci type or a connection with special symplectic holonomy. A manifold or orbifold with such a connection is called special symplectic. We show(More)
It is proved that the Lie groups E (5) 7 and E (7) 7 represented in R 56 and the Lie group EC7 represented in R 112 occur as holonomies of torsion-free affine connections. It is also shown that the moduli spaces of torsion-free affine connnections with these holonomies are finite dimensional, and that every such connection has a local symmetry group of(More)
Given the Euclidean space R2n+2 endowed with a constant symplectic structure and the standard flat connection, and given a polynomial of degree 2 on that space, Baguis and Cahen [1] have defined a reduction procedure which yields a symplectic manifold endowed with a Ricci-type connection. We observe that any symplectic manifold (M,ω) of dimension 2n (n ≥ 2)(More)
We consider cohomogeneity one homogeneous disk bundles and adress the question when these admit a nonnegatively curved1 invariant metric with normal collar, i.e., such that near the boundary the metric is the product of an interval and a normal homogeneous space. If such a bundle is not (the quotient of) a trivial bundle, then we show that its rank has to(More)