ISBN-10:
1860947727
ISBN-13:
9781860947728
Pub. Date:
06/28/2007
Publisher:
Imperial College Press
Recent Progress in Conformal Geometry

Recent Progress in Conformal Geometry

by Abbas Bahri, Yongzhong Xu

Hardcover

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Overview

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.

Product Details

ISBN-13: 9781860947728
Publisher: Imperial College Press
Publication date: 06/28/2007
Series: Icp Advanced Texts In Mathematics Series
Pages: 524
Product dimensions: 1.50(w) x 4.30(h) x 0.50(d)

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