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arXiv · 1704.06211

Chern-Dirac bundles on non-K\"ahler Hermitian manifolds

Francesco Pediconi
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Abstract

We introduce the notions of Chern-Dirac bundles and Chern-Dirac operators on Hermitian manifolds. They are analogues of classical Dirac bundles and Dirac operators, with Levi-Civita connection replaced by Chern connection. We then show that the tensor product of canonical and the anticanonical spinor bundles, called V-spinor bundle, is a bigraded Chern-Dirac bundle with spaces of harmonic spinors isomorphic to the full Dolbeault cohomology class. A similar construction establishes isomorphisms between other types of harmonic spinors and Bott-Chern, Aeppli and twisted cohomology.

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BibTeXRIS

Francesco Pediconi. 2017-04-20. Chern-Dirac bundles on non-K\"ahler Hermitian manifolds. https://arxiv.org/abs/1704.06211

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