Timeline for Harmonic spinors on closed hyperbolic manifolds
Current License: CC BY-SA 3.0
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| Apr 17, 2015 at 14:54 | comment | added | Igor Rivin | @DannyRuberman Yes, precisely. I didn't know about the results you mention, but certainly the "Bochner" obstruction does not seem to show a positive result. | |
| Apr 17, 2015 at 14:52 | comment | added | Danny Ruberman | I'm not sure if it's polite to comment negatively on specific papers, but I feel skeptical of the one you cite. There is no argument for the existence of harmonic spinors in negative curvature, other than the statement of the well-known theorem of Lichnerowicz (the converse of his claim!) that positive scalar curvature obstructs harmonic spinors. Even for surfaces, the claim that all negatively curved closed manifolds admit harmonic spinors is false, by results of Hitchin and Ammann-Dahl-Humbert. | |
| Apr 17, 2015 at 14:13 | history | answered | Igor Rivin | CC BY-SA 3.0 |