Geometric Flows of $G_2$-Structures on 3-Sasakian 7-Manifolds
Abstract
A 3-Sasakian structure on a 7-manifold may be used to define two distinct Einstein metrics: the 3-Sasakian metric and the squashed Einstein metric. Both metrics are induced by nearly parallel -structures which may also be expressed in terms of the 3-Sasakian structure. Just as Einstein metrics are critical points for the Ricci flow up to rescaling, nearly parallel -structures provide natural critical points of the (rescaled) geometric flows of -structures known as the Laplacian flow and Laplacian coflow. We study each of these flows in the 3-Sasakian setting and see that their behaviour is markedly different, particularly regarding the stability of the nearly parallel -structures. We also compare the behaviour of the flows of -structures with the (rescaled) Ricci flow.
Keywords
Cite
@article{arxiv.2210.12962,
title = {Geometric Flows of $G_2$-Structures on 3-Sasakian 7-Manifolds},
author = {Aaron Kennon and Jason D. Lotay},
journal= {arXiv preprint arXiv:2210.12962},
year = {2023}
}
Comments
23 pages and 3 figures; v2: minor changes, version accepted for publication in Journal of Geometry and Physics