Rocky Mountain Journal of Mathematics

Chern-Dirac bundles on non-Kähler 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 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.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 4 (2018), 1255-1290.

Dates
First available in Project Euclid: 30 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1538272833

Digital Object Identifier
doi:10.1216/RMJ-2018-48-4-1255

Mathematical Reviews number (MathSciNet)
MR3859758

Zentralblatt MATH identifier
06958779

Subjects
Primary: 53C27: Spin and Spin$^c$ geometry 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]

Keywords
Dirac operator non-Kähler Hermitian manifolds Chern connection

Citation

Pediconi, Francesco. Chern-Dirac bundles on non-Kähler Hermitian manifolds. Rocky Mountain J. Math. 48 (2018), no. 4, 1255--1290. doi:10.1216/RMJ-2018-48-4-1255. https://projecteuclid.org/euclid.rmjm/1538272833


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