The Dirac Spectrum
Springer Berlin (Verlag)
978-3-642-01569-4 (ISBN)
This volume surveys the spectral properties of the spin Dirac operator. After a brief introduction to spin geometry, we present the main known estimates for Dirac eigenvalues on compact manifolds with or without boundaries. We give examples where the spectrum can be made explicit and present a chapter dealing with the non-compact setting. The methods mostly involve elementary analytical techniques and are therefore accessible for Master students entering the subject. A complete and updated list of references is also included.
Basics of spin geometry.- Explicit computations of spectra.- Lower eigenvalue estimates on closed manifolds.- Lower eigenvalue estimates on compact manifolds with boundary.- Upper eigenvalue bounds on closed manifolds.- Prescription of eigenvalues on closed manifolds.- The Dirac spectrum on non-compact manifolds.- Other topics related with the Dirac spectrum.
From the reviews:
"The book under review is a very complete survey about the spectral properties of the Dirac operator on a Spin manifold. Intended for non-specialists of spin geometry, it is accessible for masters students ... . All throughout the book, classical and recent results are given with complete proofs and an exhaustive bibliography is provided ... this work is useful to researchers in spin geometry and as a reference to learn the Dirac operator." (Julien Roth, Mathematical Reviews, Issue 2010 a)
"This memory is a survey on the spectral properties of the Dirac operator defined by a spin structure on a Riemannian manifold. I think that it can be used as a valuable guide to get introduced in this subject. The book is self-contained once some basic concepts of differential geometry are known, like vector bundles, Lie groups, principal bundles, connections, curvature, etc." (Jesus A. Álvarez López, Zentralblatt MATH, Vol. 1186, 2010)
| Erscheint lt. Verlag | 15.6.2009 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | XV, 156 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 580 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | 35P15, 53C27, 58C40, 58J32, 58J50 • Global Analysis • manifold • Partial differential equations • Spectral Geometry • Spin Geometry • Spinor |
| ISBN-10 | 3-642-01569-7 / 3642015697 |
| ISBN-13 | 978-3-642-01569-4 / 9783642015694 |
| Zustand | Neuware |
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