Institute for Mathematical Physics Hyper{kk Ahler Hierarchies and Their Twistor Theory Hyper-kk Ahler Hierarchies and Their Twistor Theory

Hyper - K ahler

A twistor construction of the hierarchy associated with the hyper-KK ahler equations on a metric (the anti-self-dual Einstein vacuum equations, ASDVE, in four dimensions) is given. The recursion operator R is constructed and used to build an innnite-dimensional symmetry algebra and in particular higher ows for the hyper-KK ahler equations. It is shown that R acts on the twistor data by multipli...

Deformations of Hypercomplex Structures

Twistor theory shows that deformations of a hypercomplex manifold correspond to deformations of a canonically constructed holomorphic map from the twistor space of the hypercomplex manifold onto the complex projective line. Applying Horikawa's theory of deformations of maps, we calculate deformations of compact quotients and twists of the associated bundles of quaternionic manifolds. In particu...

Institute for Mathematical Physics Examples of Hyper-kk Ahler Connections with Torsion

Institute for Mathematical Physics Einstein{weyl Structures from Hyper{kk Ahler Metrics with Conformal Killing Vectors

Quaternionic K Ahler Metrics and Nilpotent Orbits

Given a geometric structure on a manifold it is natural to ask what are the symmetries of that structure and what are the examples of such structures with a big group of symmetries. In this talk I wish to start by discussing such questions for quaternionic KK ahler manifolds. Let M be a quaternionic KK ahler manifold, that is a manifold whose holonomy is contained in Sp(n) Sp(1), the subgroup o...