arXiv 2111.135412021-11math.DGmath.GT

Dolbeault-type complexes on $G_2$- and $\mathrm{Spin}(7)$-manifolds

Xue Zhang

英文摘要：

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.

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