The space of closed $G2$-structures. II. concavity and hypersymplectic structures
Differential Geometry
2025-07-29 v1 Symplectic Geometry
Abstract
In the space of closed -structures equipped with Bryant's Dirichlet-type metric, we continue to utilise the geodesic, constructed in our previous article, to show that, under a normalisation condition Hitchin's volume functional is geodesically concave and the Laplacian flow decreases the length. Furthermore, we also construct various examples of hyper-symplectic manifolds on geodesic concavity.
Keywords
Cite
@article{arxiv.2507.20456,
title = {The space of closed $G2$-structures. II. concavity and hypersymplectic structures},
author = {Kai Zheng},
journal= {arXiv preprint arXiv:2507.20456},
year = {2025}
}