CiNii 図書 - Recent progress in conformal geometry

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.

Sign-Changing Yamabe-Type Problems: General Introduction
Results and Conditions
Conjecture 2 and Sketch of the Proof of Theorem 1
Outline
The Difference of Topology
Open Problems
Preliminary Estimates and Expansions, the Principal Terms
Preliminary Estimates
Proof of the Morse Lemma at Infinity when the Concentrations are Comparable
Proof of the Morse Lemma at Infinity
Contact Form Geometry: General Introduction
On the Dynamics of a Contact Structure Along a Vector Field of Its Kernel
Appendix 1
The Normal Form of ( , ) Near an Attractive Periodic Orbit of
Compactness
Transmutations
On the Morse Index of a Functional Arising in Contact Form Geometry
and other chapters.

「Nielsen BookData」より

Recent progress in conformal geometry

著者

書誌事項

大学図書館所蔵全22件

この図書・雑誌をさがす

注記

内容説明・目次

関連文献： 1件中 1-1を表示

詳細情報

書き出し