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2018 Chern-Dirac bundles on non-Kähler Hermitian manifolds
Francesco Pediconi
Rocky Mountain J. Math. 48(4): 1255-1290 (2018). DOI: 10.1216/RMJ-2018-48-4-1255

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 the Levi-Civita connection replaced by the Chern connection. We then show that the tensor product of the canonical and the anticanonical spinor bundles, called the $\mathcal{V} $-spinor bundle, is a bigraded Chern-Dirac bundle with spaces of harmonic sections isomorphic to the full Dolbeault cohomology class. A similar construction establishes isomorphisms among other types of harmonic sections of the $\mathcal{V} $-spinor bundle and twisted cohomology.

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Francesco Pediconi. "Chern-Dirac bundles on non-Kähler Hermitian manifolds." Rocky Mountain J. Math. 48 (4) 1255 - 1290, 2018. https://doi.org/10.1216/RMJ-2018-48-4-1255

Information

Published: 2018
First available in Project Euclid: 30 September 2018

zbMATH: 06958779
MathSciNet: MR3859758
Digital Object Identifier: 10.1216/RMJ-2018-48-4-1255

Subjects:
Primary: 53C27, 53C55

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 4 • 2018
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