Analysis on Kähler and Lorentzian manifolds - Archive ouverte HAL Accéder directement au contenu
Hdr Année : 2013

Analysis on Kähler and Lorentzian manifolds

Nicolas Ginoux

Résumé

This habilitation thesis deals with the interactions between geometry of and analysis on smooth manifolds in different situations. Chapter 1 summarises all the results obtained in the next chapters. Chapter 2 deals with the spectrum of the Dirac operator of the Berger metrics on a 3-dimensional space. Estimates on the smallest eigenvalues of twisted Dirac operators on the complex projective space are computed and their limiting-case discussed in chapter 3. Chapter 4 focuses on a purely geometric question of classifying those Kähler spin manifolds with imaginary Kählerian Killing spinors. In chapter 5, we address the Yamabe problem on globally hyperbolic spacetimes. Chapter 6 is concerned with locally covariant quantization of fields for a large class of differential operators on spacetimes.
Fichier principal
Vignette du fichier
ginoux_habil.pdf (1.32 Mo) Télécharger le fichier

Dates et versions

tel-01266075 , version 1 (02-02-2016)

Identifiants

  • HAL Id : tel-01266075 , version 1

Citer

Nicolas Ginoux. Analysis on Kähler and Lorentzian manifolds. Differential Geometry [math.DG]. Universität Regensburg, 2013. ⟨tel-01266075⟩

Collections

TDS-MACS
133 Consultations
445 Téléchargements

Partager

Gmail Facebook X LinkedIn More