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Bahri A., Xu Y. — Recent Progress in Conformal Geometry
Bahri A., Xu Y. — Recent Progress in Conformal Geometry



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Название: Recent Progress in Conformal Geometry

Авторы: Bahri A., Xu Y.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Неизвестно

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Год издания: 2007

Количество страниц: 522

Добавлена в каталог: 29.03.2020

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