Balanced Hermitian metrics from SU(2)-structures

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 $n=3,4$, 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).

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• Geometric Model for Complex Non-Kaehler Manifolds with SU(3) Structure
• Compactifications of Heterotic Theory on Non-Kahler Complex Manifolds: I
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Cited by in corpus (5)

• Non-Kaehler Heterotic String Solutions with non-zero fluxes and non-constant dilaton
• Compact supersymmetric solutions of the heterotic equations of motion in dimension 5
• Mink${}_3\times S^3$ solutions of type II supergravity
• On the existence of balanced metrics on six-manifolds of cohomogeneity one
• The Mean Curvature of Special Lagrangian 3-folds in SU(3)-Structures with Torsion