Recent Progress in Conformal Geometry (Hardcover) (ISBN-13: 9781860947728)

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.

Author: Abbas Bahri,Yongzhong Xu
ISBN-10: 1860947727
ISBN-13: 9781860947728
Publisher: Imperial College Press
Language: English
Published: 06/01/2007
Pages: 524
Format: Hardcover
Weight: 3.29lbs
Size: 8.82h x 6.41w x 1.34d