Chern-Dirac bundles on non-K\"ahler Hermitian manifolds
Differential Geometry
2017-11-29 v2
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.
Keywords
Cite
@article{arxiv.1704.06211,
title = {Chern-Dirac bundles on non-K\"ahler Hermitian manifolds},
author = {Francesco Pediconi},
journal= {arXiv preprint arXiv:1704.06211},
year = {2017}
}
Comments
23 pages; some minor changes, accepted for publication in Rocky Mountain J. Math