The Einstein condition on nearly K\"ahler six-manifolds
Differential Geometry
2020-10-26 v3
Abstract
We review basic facts on the structure of nearly K\"ahler manifolds, focussing in particular on the six-dimensional case. A self-contained proof that nearly K\"ahler six-manifolds are Einstein is given by combining different known results. We finally rephrase the definition of nearly K\"ahler six-manifold in terms of a pair of partial differential equations.
Cite
@article{arxiv.2002.04673,
title = {The Einstein condition on nearly K\"ahler six-manifolds},
author = {Giovanni Russo},
journal= {arXiv preprint arXiv:2002.04673},
year = {2020}
}
Comments
23 pages. General minor revisions, Remark 5.4 and two references added. To appear in Expositiones Mathematicae