Eigenvalue pinching on $\text{spin}^c$ manifolds

Saskia Roos

doi:10.1016/j.geomphys.2016.11.006

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arXiv · 1604.01596

Eigenvalue pinching on $\text{spin}^c$ manifolds

Saskia Roos

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Abstract

We derive various pinching results for small Dirac eigenvalues using the classification of $\text{spin}^c$ and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for $\text{spin}^c$ manifolds which involves a general study on convergence of Riemannian manifolds with a principal $\mathbb{S}^1$-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal $\mathbb{S}^1$-bundle on $\text{spin}^c$ manifolds with Killing spinors.

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Saskia Roos. 2016-04-06. Eigenvalue pinching on $\text{spin}^c$ manifolds. https://doi.org/10.1016/j.geomphys.2016.11.006

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