NORMALIZED WEYL-TYPE ⋆-PRODUCT ON KÄHLER MANIFOLDS

Normalized Weyl-type ⋆-product on Kähler manifolds

We define a normalized Weyl-type ⋆-product on general Kähler manifolds. Expanding this product perturbatively we show that the cumbersome term, which appears in a Berezin-type product, does not appear at least in the first order of h̄. This means a normalization factor, which is introduced by Reshetikhin and Takhtajan for a Berezin-type product, is unnecessary for our Weyl-type product at that o...

Normalized Moyal-type ⋆-product on Kähler manifolds

We define a normalized Moyal-type ⋆-product on general Kähler manifolds. Expanding this product perturbatively we show that the cumbersome term, which appears in a Berezin-type product, does not appear at least in the first order of h̄. This means a normalization factor, which is introduced by Reshetikhin and Takhtajan for a Berezin-type product, is unnecessary for our Moyal-type product at that...

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...

0 Ricci flow on Kähler manifolds

Weyl Laws on Open Manifolds

Under suitable invertibility hypothesis, the spectrum of the Dirac operator on certain open spin Riemannian manifolds is discrete, and obeys a growth law depending qualitatively on the (in)finiteness of the volume.