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A Spinorial Approach to Riemannian a...

Bourguignon, Jean-Pierre,

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A Spinorial Approach to Riemannian and Conformal Geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	A Spinorial Approach to Riemannian and Conformal Geometry/ Jean-Pierre Bourguignon, Oussama Hijazi, Jean-Louis Milhorat, Andrei Moroianu, Sergiu Moroianu
Author:	Bourguignon, Jean-Pierre,
other author:	Hijazi, Oussama,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2015,
Description:	1 online resource (462 pages)
Subject:	Differential & Riemannian geometry -
Online resource:	https://doi.org/10.4171/136
Online resource:	https://www.ems-ph.org/img/books/bourguignon_mini.jpg
ISBN:	9783037196366

A Spinorial Approach to Riemannian and Conformal Geometry
Bourguignon, Jean-Pierre,

A Spinorial Approach to Riemannian and Conformal Geometry[electronic resource] /Jean-Pierre Bourguignon, Oussama Hijazi, Jean-Louis Milhorat, Andrei Moroianu, Sergiu Moroianu - Zuerich, Switzerland :European Mathematical Society Publishing House,2015 - 1 online resource (462 pages) - EMS Monographs in Mathematics (EMM) ;2523-5192.

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

The book gives an elementary and comprehensive introduction to Spin Geometry, with particular emphasis on the Dirac operator which plays a fundamental role in differential geometry and mathematical physics. After a self-contained presentation of the basic algebraic, geometrical, analytical and topological ingredients, a systematic study of the spectral properties of the Dirac operator on compact spin manifolds is carried out. The classical estimates on eigenvalues and their limiting cases are discussed next, highlighting the subtle interplay of spinors and special geometric structures. Several applications of these ideas are presented, including spinorial proofs of the Positive Mass Theorem or the classification of positive Kähler-Einstein contact manifolds. Representation theory is used to explicitly compute the Dirac spectrum of compact symmetric spaces. The special features of the book include a unified treatment of Spin$^\mathrm c$ and conformal spin geometry (with special emphasis on the conformal covariance of the Dirac operator), an overview with proofs of the theory of elliptic differential operators on compact manifolds based on pseudodifferential calculus, a spinorial characterization of special geometries, and a self-contained presentation of the representation-theoretical tools needed in order to apprehend spinors. This book will help advanced graduate students and researchers to get more familiar with this beautiful, though not sufficiently known, domain of mathematics with great relevance to both theoretical physics and geometry.

ISBN: 9783037196366

Standard No.: 10.4171/136doiSubjects--Topical Terms:

3480810
Differential & Riemannian geometry

A Spinorial Approach to Riemannian and Conformal Geometry
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245 1 0 $a A Spinorial Approach to Riemannian and Conformal Geometry $h [electronic resource] / $c Jean-Pierre Bourguignon, Oussama Hijazi, Jean-Louis Milhorat, Andrei Moroianu, Sergiu Moroianu
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520 $a The book gives an elementary and comprehensive introduction to Spin Geometry, with particular emphasis on the Dirac operator which plays a fundamental role in differential geometry and mathematical physics. After a self-contained presentation of the basic algebraic, geometrical, analytical and topological ingredients, a systematic study of the spectral properties of the Dirac operator on compact spin manifolds is carried out. The classical estimates on eigenvalues and their limiting cases are discussed next, highlighting the subtle interplay of spinors and special geometric structures. Several applications of these ideas are presented, including spinorial proofs of the Positive Mass Theorem or the classification of positive Kähler-Einstein contact manifolds. Representation theory is used to explicitly compute the Dirac spectrum of compact symmetric spaces. The special features of the book include a unified treatment of Spin$^\mathrm c$ and conformal spin geometry (with special emphasis on the conformal covariance of the Dirac operator), an overview with proofs of the theory of elliptic differential operators on compact manifolds based on pseudodifferential calculus, a spinorial characterization of special geometries, and a self-contained presentation of the representation-theoretical tools needed in order to apprehend spinors. This book will help advanced graduate students and researchers to get more familiar with this beautiful, though not sufficiently known, domain of mathematics with great relevance to both theoretical physics and geometry.
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700 1 $a Moroianu, Sergiu, $e author. $3 3481108
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