Recent Progress In Conformal Geometry

Abbas Bahri, Yongzhong Xu

• Publisher: ICP
• Year: 2007
• Print ISBN: 9781860947728, 9781860947728
• eBook ISBN: 9781860948602
• Topic: Mathematics
• Subtopic: Analytic Geometry
• Index: Mathematics

This book presents a new front of research in conformal geometry, on sign-changing Yamabe-type problems and contact form geometry in particular. New ground is broken with the establishment of a Morse lemma at infinity for sign-changing Yamabe-type problems. This family of problems, thought to be out of reach a few years ago, becomes a family of problems which can be studied: the book lays the foundation for a program of research in this direction.In contact form geometry, a cousin of symplectic geometry, the authors prove a fundamental result of compactness in a variational problem on Legrendrian curves, which allows one to define a homology associated to a contact structure and a vector field of its kernel on a three-dimensional manifold. The homology is invariant under deformation of the contact form, and can be read on a sub-Morse complex of the Morse complex of the variational problem built with the periodic orbits of the Reeb vector-field. This book introduces, therefore, a practical tool in the field, and this homology becomes computable.

Table of contents

• Contents
• Preface A. Bahri and Y. Xu
• 1. Sign-Changing Yamabe-Type Problems
• Bibliography
• 2. Contact Form Geometry
• Bibliography