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 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 V-spinor bundle and twisted cohomology.

Chern-Dirac bundles on non-Kähler Hermitian manifolds / Pediconi, F. - In: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS. - ISSN 0035-7596. - STAMPA. - 48:(2018), pp. 1255-1290. [10.1216/RMJ-2018-48-4-1255]

Chern-Dirac bundles on non-Kähler Hermitian manifolds

Pediconi, F
2018

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 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 V-spinor bundle and twisted cohomology.
48
1255
1290
Pediconi, F
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/1280623
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