Eigenvalue Estimates on Quaternion-Kähler Manifolds

Kähler (& Hyper-kähler) Manifolds

These notes are based on two talks given at the Arithmetic & Algebraic Geometry Seminar of the Korteweg-de Vriesinstituut for mathematics of the Universiteit van Amsterdam. They are intended to give a short introduction to the theory of Kähler manifolds, with a slight focus of applicability to the subject of K3 surfaces. However, they also include other interesting results not related to K3 sur...

Tensor supermultiplets and toric quaternion - Kähler geometry †

We review the relation between 4n-dimensional quaternion-Kähler metrics with n + 1 abelian isometries and superconformal theories of n + 1 tensor supermultiplets. As an application we construct the class of eight-dimensional quaternion-Kähler metrics with three abelian isometries in terms of a single function obeying a set of linear second-order partial differential equations. Talk given by F.S...

0 Ricci flow on Kähler manifolds

Ricci Flow on Kähler-einstein Manifolds

Some Remarks on Quaternion-hermitian Manifolds

Nearly-quaternionic KK ahler manifolds of dimension at least 8 are shown to be quaternionic KK ahler. Restrictions on the covariant derivative of the fundamental four-form of a semi-quaternionic KK ahler are also found.