A Spinorial Approach to Riemannian and Conformal Geometry
Jean-Pierre Bourguignon
IHÉS, Bures-sur-Yvette, FranceOussama Hijazi
Université de Lorraine, Nancy, FranceJean-Louis Milhorat
Université de Nantes, FranceAndrei Moroianu
Université de Versailles-St Quentin, FranceSergiu Moroianu
Institutul de Matematică al Academiei Române, București, Romania
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| FrontmatterDownload pp. i–iv | |
| ContentsDownload pp. v–ix | |
| IntroductionDownload pp. 1–8 | |
| Part I Basic spinorial materialp. 9 | |
| 1 | Algebraic aspectspp. 11–38 |
| 2 | Geometrical aspectspp. 39–84 |
| 3 | Topological aspectspp. 85–97 |
| 4 | Analytical aspectspp. 99–123 |
| Part II Lowest eigenvalues of the Dirac operator on closed spin manifoldsp. 125 | |
| 5 | Lower eigenvalue bounds on Riemannian closed spin manifoldspp. 127–159 |
| 6 | Lower eigenvalue bounds on Kähler manifoldspp. 161–173 |
| 7 | Lower eigenvalue bounds on quaternion-Kähler manifoldspp. 175–211 |
| Part III Special spinor fields and geometriesp. 213 | |
| 8 | Special spinors on Riemannian manifoldspp. 215–249 |
| 9 | Special spinors on conformal manifoldspp. 251–264 |
| 10 | Special spinors on Kähler manifoldspp. 265–277 |
| 11 | Special spinors on quaternion-Kähler manifoldspp. 279–299 |
| Part IV Dirac spectra of model spacesp. 301 | |
| Introduction of Dirac spectra of model spacesDownload p. 303 | |
| 12 | A brief survey on representation theory of compact groupspp. 305–368 |
| 13 | Symmetric space structure of model spacespp. 369–377 |
| 14 | Riemannian geometry of model spacespp. 379–393 |
| 15 | Explicit computations of the Dirac spectrumpp. 395–419 |
| Bibliographypp. 421–449 | |
| Indexpp. 451–452 |