On the existence of balanced metrics on six-manifolds of cohomogeneity one

We 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 th...

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Bibliographic Details
Published in:Annals of global analysis and geometry 2022-03, Vol.61 (2), p.309-331
Main Authors: Alonso, Izar, Salvatore, Francesca
Format: Article
Language:English
Subjects:
Analysis
Differential Geometry
Geometry
Global Analysis and Analysis on Manifolds
Lie groups
Mathematical Physics
Mathematics
Mathematics and Statistics
Orbits
String theory
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Summary:We 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 SU ( 3 ) -structures which are invariant under a cohomogeneity one action on simply connected six-manifolds.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-021-09807-z