Fr\"olicher-Nijenhuis bracket on manifolds with special holonomy
Differential Geometry
2019-02-23 v1
Abstract
In this article, we summarize our recent results on the study of manifolds with special holonomy via the Fr\"olicher-Nijenhuis bracket. This bracket enables us to define the Fr\"olicher-Nijenhuis cohomologies which are analogues of the and the Dolbeault cohomologies in K\"ahler geometry, and assigns an -algebra to each associative submanifold. We provide several concrete computations of the Fr\"olicher-Nijenhuis cohomology.
Keywords
Cite
@article{arxiv.1810.12714,
title = {Fr\"olicher-Nijenhuis bracket on manifolds with special holonomy},
author = {Kotaro Kawai and Hông Vân Lê and Lorenz Schwachhöfer},
journal= {arXiv preprint arXiv:1810.12714},
year = {2019}
}
Comments
14 pages, To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics". arXiv admin note: text overlap with arXiv:1703.05133