03301nam a22004455a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168072001700185084003600202100003900238245018300277260008200460300003400542336002600576337002600602338003600628347002400664490005300688506006500741520158300806650004702389650003502436650003102471650004302502650004102545650004002586700003002626700003502656700003102691700003102722856003202753856007002785194-150629CH-001817-320150629234504.0a fot ||| 0|cr nn mmmmamaa150629e20150629sz fot ||| 0|eng d a978303719636670a10.4171/1362doi ach0018173 7aPBMP2bicssc 7aPBKJ2bicssc a53-xxa17-xxa34-xxa35-xx2msc1 aBourguignon, Jean-Pierre,eauthor.10aA Spinorial Approach to Riemannian and Conformal Geometryh[electronic resource] /cJean-Pierre Bourguignon, Oussama Hijazi, Jean-Louis Milhorat, Andrei Moroianu, Sergiu Moroianu3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (462 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Monographs in Mathematics (EMM) ;x2523-51921 aRestricted to subscribers:uhttp://www.ems-ph.org/ebooks.php aThe 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.07aDifferential & Riemannian geometry2bicssc07aDifferential equations2bicssc07aDifferential geometry2msc07aNonassociative rings and algebras2msc07aOrdinary differential equations2msc07aPartial differential equations2msc1 aHijazi, Oussama,eauthor.1 aMilhorat, Jean-Louis,eauthor.1 aMoroianu, Andrei,eauthor.1 aMoroianu, Sergiu,eauthor.40uhttps://doi.org/10.4171/136423cover imageuhttp://www.ems-ph.org/img/books/bourguignon_mini.jpg