Dolbeault-type complexes on $G_2$- and $\mathrm{Spin}(7)$-manifolds
Differential Geometry
2022-01-12 v2 Geometric Topology
Abstract
There are three types of Dolbeault complexes arising from representations of holonomy group on a Riemannian manifold, two of which are dual to each other. Such a complex is elliptic if and only if its generator satisfies an algebraic condition. As applications, we give all Dolbeault complexes on a compact Riemannian manifold with exceptional holonomy. Each cohomology can be described by harmonic forms.
Keywords
Cite
@article{arxiv.2111.13541,
title = {Dolbeault-type complexes on $G_2$- and $\mathrm{Spin}(7)$-manifolds},
author = {Xue Zhang},
journal= {arXiv preprint arXiv:2111.13541},
year = {2022}
}