The Dirac operator on spaces with conical singularities and positive scalar curvatures

Chou, Arthur Weichung

doi:10.1090/S0002-9947-1985-0779050-8

The Dirac operator on spaces with conical singularities and positive scalar curvatures
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Trans. Amer. Math. Soc. 289 (1985), 1-40 Request permission

Abstract:

We study, in the spirit of Jeff Cheeger, the Dirac operator on a space with conical singularities. We obtain a Bochner-type vanishing theorem and prove an index theorem in the singular case. Also, the relationship with manifolds with boundary is explored. In the Appendix two methods of deforming the metric near the boundary are established and applied to obtain several new results on constructing complete metrics with positive scalar curvature.

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