Abstract
AbstractWe consider balanced metrics on complex manifolds with holomorphically trivial canonical bundle, most commonly known as balanced SU(n)-structures. Such structures are of interest for both Hermitian geometry and string theory, since they provide the ideal setting for the Hull–Strominger system. In this paper, we provide a non-existence result for balanced non-Kähler $$\text {SU}(3)$$
SU
(
3
)
-structures which are invariant under a cohomogeneity one action on simply connected six-manifolds.
Funder
engineering and physical sciences research council
gnsaga of indam
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Analysis
Reference34 articles.
1. Alexandrino, M.M., Bettiol, R.G.: Lie Groups and Geometric Aspects of Isometric Actions. Springer, Berlin (2015)
2. Alexandrov, B., Ivanov, S.: Vanishing theorems on Hermitian manifolds. Differ. Geom. Appl. 14, 251–265 (2001)
3. Bedulli, L., Vezzoni, L.: The Ricci tensor of SU(3)-manifolds. J. Geom. Phys. 57, 1125–1146 (2007)
4. Bedulli, L., Vezzoni, L.: A parabolic flow of balanced metrics. J. Reine Angew. Math. 723, 79–99 (2017)
5. Bérard Bergery, L.: Sur des nouvelles varietes Riemanniennes d’Einstein, Publ. de Inst. E. Cartan 6 (1982), 1–60