Elliptic complexes on $G_2$ and $\mathrm{Spin}(7)-$manifolds
Year: 2021
Type: preprint
Abstract: There are three types of generalized de Rham complexes arising from representations of holonomy group on a smooth Riemannian manifold, two of which are dual to each other. We prove that a complex is elliptic if and only if its generator satisfies an algebraic condition. As applications, we give all elliptic complexes on a Riemannian manifold with exceptional holonomy.
Source: arXiv (Cornell University)
Author: Xue Zhang
Institution: Tsinghua University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3215161620