Eigenvalue pinching on manifolds
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文摘
We derive various pinching results for small Dirac eigenvalues using the classification of spincspinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spincspinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1S1-bundle on spincspinc manifolds with Killing spinors.