Oliver Baues

Realisation of special Kahler manifolds as parabolic spheres

We prove that any simply connected special Kaihler manifold admits a canonical immersion as a parabolic affine hypersphere. As an application, we associate a parabolic affine hypersphere to any nondegenerate holomorphic function. We also show that a classical result of Calabi and Pogorelov on parabolic spheres implies Lus theorem on complete special Kaihler manifolds with a positive definite metric.

Automorphism groups of polycyclic-by-finite groups and arithmetic groups

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences of K(Γ,1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory.

Prehomogeneous affine representations and flat pseudo-Riemannian manifolds

The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the heart of our presentation is a development of the theory of characteristic classes and characters of prehomogeneous affine representations. We give applications concerning flat affine, as well as Pseudo-Riemannian and symplectic affine flat manifolds.We investigate the integrability of natural almost complex structures on the twistor space of an almost para-quaternionic manifold as well as the integrability of natural almost paracomplex structures on the reflector space of an almost para-quaternionic manifold constructed with the help of a para-quaternionic connection. We show that if there is an integrable structure it is independent on the para-quaternionic connection. In dimension four, we express the anti-self-duality condition in terms of the Riemannian Ricci forms with respect to the associated para-quaternionic structure.Under the action of the c-map, special K¨ahler manifolds are mapped into a class of quaternion-K¨ahler spaces. We explicitly construct the corresponding Swann bundle or hyperk¨ahler cone, and determine the hyperk¨ahler potential in terms of the prepotential of the special K¨ahler geometry.We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skew-symmetric Nijenhuis tensor. We investigate up to what extent the Nijenhuis tensor fails to be parallel with respect to the characteristic connexion. This is naturally described by means of an extension of the notion of Killing form to almost Hermitian geometry. In this context, we also make an essentially self-contained survey of nearly-Kaehler geometry, but from the perspective of non-integrable holonomy systems.An almost para-CR structure on a manifold

The deformation of flat affine structures on the two-torus

M

Flat pseudo-Riemannian homogeneous spaces with non-abelian holonomy group

is given by a distribution

Aspherical Kähler manifolds with solvable fundamental group

HM \subset TM

Proper affine hyperspheres which fiber over projective special Kähler manifolds

together with a field

Is the deformation space of complete affine structures on the 2-torus smooth?

K \in \Gamma({\rm End}(HM))

Symplectic Lie Groups I-III

of involutive endomorphisms of

Seifert fiberings and collapsing of infrasolv spaces

HM