Balanced Hermitian metrics from SU(2)-structures
Differential Geometry
2009-11-13 v1
Abstract
We study the intrinsic geometrical structure of hypersurfaces in 6-manifolds carrying a balanced Hermitian SU(3)-structure, which we call {\em balanced} SU(2)-{\em structures}. We provide conditions which imply that such a 5-manifold can be isometrically embedded as a hypersurface in a manifold with a balanced SU(3)-structure. We show that any 5-dimensional compact nilmanifold has an invariant balanced SU(2)-structure as well as new examples of balanced Hermitian SU(3)-metrics constructed from balanced SU(2)-structures. Moreover, for , we present examples of compact manifolds, endowed with a balanced SU(n)-structure, such that the corresponding Bismut connection has holonomy equal to SU(n).
Cite
@article{arxiv.0808.1201,
title = {Balanced Hermitian metrics from SU(2)-structures},
author = {Marisa Fernández and Adriano Tomassini and Luis Ugarte and Raquel Villacampa},
journal= {arXiv preprint arXiv:0808.1201},
year = {2009}
}