On Bochner Flat Kähler B-Manifolds

BOCHNER - KÄHLER METRICS 3 Theorem

A Kähler metric is said to be Bochner-Kähler if its Bochner curvature vanishes. This is a nontrivial condition when the complex dimension of the underlying manifold is at least 2. In this article it will be shown that, in a certain well-defined sense, the space of Bochner-Kähler metrics in complex dimension n has real dimension n+1 and a recipe for an explicit formula for any Bochner-Kähler met...

Twistor Spaces of Non-flat Bochner-kähler Manifolds

This can be compared to the fact that a conformally flat manifold of dimension n > 2 is locally conformal to a region of the sphere of the same dimension. In twistor theory, it is well-known that an even dimensional conformally flat manifold has an integrable twistor space ([7], [6], [1], [3]). It is interesting, as an analogy, that a Bochner-Kähler manifold has integrable twistor spaces define...

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...

Classification of Bochner Flat Kähler Manifolds by Heisenberg, Spherical CR Geometry

A Bochner flat Kähler manifold is a Kähler manifold with vanishing Bochner curvature tensor. We shall give a uniformization of Bochner flat Kähler manifolds. One of the aims of this paper is to give a correction to the proof of our previous paper [9] concerning uniformization of Bochner flat Kähler manifolds. A Bochner flat locally conformal Kähler manifold is a locally conformal Kähler manifol...

0 Ricci flow on Kähler manifolds