| Recent Progress in Conformal Geometry Contributor(s): Bahri, Abbas (Author), Xu, Yongzhong (Author) |
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ISBN: 1860947727 ISBN-13: 9781860947728 Publisher: Imperial College Press OUR PRICE: $186.20 Product Type: Hardcover Published: June 2007 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Analytic - Mathematics | Mathematical Analysis |
| Dewey: 516.35 |
| Series: ICP Advanced Texts in Mathematics |
| Physical Information: 1.34" H x 6.41" W x 8.82" (3.29 lbs) 524 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |