The Kähler geometry of Bott 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...

Classification of Real Bott Manifolds

A real Bott manifold is the total space of a sequence of RP 1 bundles starting with a point, where each RP 1 bundle is the projectivization of a Whitney sum of two real line bundles. A real Bott manifold is a real toric manifold which admits a flat riemannian metric. An upper triangular (0, 1) matrix with zero diagonal entries uniquely determines such a sequence of RP 1 bundles but different ma...

Lectures on Kähler Geometry

Cohomological Rigidity of Real Bott Manifolds

Abstract. A real Bott manifold is the total space of iterated RP 1 bundles starting with a point, where each RP 1 bundle is projectivization of a Whitney sum of two real line bundles. We prove that two real Bott manifolds are diffeomorphic if their cohomology rings with Z/2 coefficients are isomorphic. A real Bott manifold is a real toric manifold and admits a flat riemannian metric invariant u...

On Nearly Kähler Geometry *

We consider complete nearly Kähler manifolds with the canonical Hermitian connection. We prove some metric properties of strict nearly Kähler manifolds and give a sufficient condition for the reducibility of the canonical Hermitian connection. A holonomic condition for a nearly Kähler manifold to be a twistor space over a quaternionic Kähler manifold is given. This enables us to give classifica...