A Construction of Non-Kähler Calabi-Yau Manifolds and New Solutions to the Strominger System

Abstract

We propose a new construction of compact non-Kähler Calabi-Yau manifolds with balanced metrics and study the Strominger system on them. In particular, we obtain explicit solutions to the Strominger system with degeneracies on ${\Sigma }_g\times T^4$, where ${\Sigma }_g$ is an immersed minimal surface of genus $g\ge 3$ in $T^3$.

17 pages, comments are welcome! Updates in v2: small revisions with new references added

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• Special Hermitian metrics on compact solvmanifolds
• Stable Forms, Vector Cross Products and Their Applications in Geometry
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Cited by in corpus (21)

• The Fu-Yau equation with negative slope parameter
• Lectures on the Strominger system
• The Anomaly flow over Riemann surfaces
• Anomaly Flow and T-Duality
• The Anomaly flow and the Fu-Yau equation
• The Heterotic-Ricci flow and its three-dimensional solitons
• New curvature flows in complex geometry
• Special Lagrangian cycles and Calabi-Yau transitions
• The Hull-Strominger system and the Anomaly flow on a class of solvmanifolds
• Geometric flows and Strominger systems
• Moduli identification methods in Type II compactifications
• A flow of conformally balanced metrics with Kähler fixed points
• The Anomaly flow on nilmanifolds
• The Anomaly flow on unimodular Lie groups
• On the existence of balanced metrics on six-manifolds of cohomogeneity one
• Balanced and Aeppli Parameters for the Heterotic Moduli
• Higher dimensional generalizations of twistor spaces
• An example of non-Kähler Calabi-Yau fourfold
• $T^4$ fibrations over Calabi-Yau two-folds and non-Kahler manifolds in string theory
• Special Hermitian structures on suspensions
• Convergence of Hermitian manifolds and the Type IIB flow