Recent Progress in Conformal Geometry
Abbas Bahri, Yongzhong Xu,
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.
Kategori:
Tahun:
2007
Edisi:
1
Penerbit:
Imperial College Press - World Scientific
Bahasa:
english
Halaman:
524
ISBN 10:
186094860X
ISBN 13:
9781860948602
Nama seri:
ICP Advanced Texts in Mathematics
File:
PDF, 3.17 MB
IPFS:
,
english, 2007