### 3-K-contact Wolf spaces

The aim of this paper is to give an easy explicit description of 3-K-contact structures on SO(3)-principal fibre bundles over Wolf quaternionic Kähler manifolds.

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The aim of this paper is to give an easy explicit description of 3-K-contact structures on SO(3)-principal fibre bundles over Wolf quaternionic Kähler manifolds.

We study 3-submersions from a QR-hypersurface of a quaternionic Kähler manifold onto an almost quaternionic hermitian manifold. We also prove the non-existence of quaternionic submersions between quaternionic Kähler manifolds which are not locally hyper-Kähler.

∗Research supported in part by NSF grant INT-9903302.In previous work a hyperbolic twistor space over a paraquaternionic Kähler manifold was defined, the fibre being the hyperboloid model of the hyperbolic plane with constant curvature −1. Two almost complex structures were defined on this twistor space and their properties studied. In the present paper we consider a twistor space over a paraquaternionic Kähler manifold with fibre given by the hyperboloid of 1-sheet, the anti-de-Sitter plane...

The set of all Abelian simply transitive subgroups of the affine group naturally corresponds to the set of real solutions of a system of algebraic equations. We classify all simply transitive subgroups of the symplectic affine group by constructing a model space for the corresponding variety of solutions. Similarly, we classify the complete global model spaces for flat special Kähler manifolds with a constant cubic form.

We consider almost hyper-Hermitian structures on principal fibre bundles with one-dimensional fiber over manifolds with almost contact 3-structure and study relations between the respective structures on the total space and the base. This construction suggests the definition of a new class of almost contact 3-structure, which we called trans-Sasakian, closely connected with locally conformal quaternionic Kähler manifolds. Finally we give a family of examples of hypercomplex manifolds which are not...

We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus $T$ with a complex line $\u2102$, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to $T\times {\mathbb{P}}^{1}$. The converse statement is also true, namely a holomorphic bundle on $T\times {\mathbb{P}}^{1}$ which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic instanton....

Let $M$ be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space $Z$ admits a natural metric. The aim of this article is to study properties of complex structures on $Z$ which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on $M$ (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space $Z$.

We prove estimates for the sectional curvature of hyperkähler quotients and give applications to moduli spaces of solutions to Nahm’s equations and Hitchin’s equations.

Tubular neighborhoods play an important role in modern differential topology. The main aim of the paper is to apply these constructions to geometry of structures on Riemannian manifolds. Deformations of tensor structures on a normal tubular neighborhood of a submanifold in a Riemannian manifold are considered in section 1. In section 2, this approach is used to obtain a Kählerian structure on the corresponding normal tubular neighborhood of the null section in the tangent bundle TM of a smooth manifold...

The original version of the article was published in Central European Journal of Mathematics, 2008, 6(2), 191–203, DOI: 10.2478/s11533-008-0026-8. Unfortunately, the original version of this article contains a mistake, which we correct here.