A flow of conformally balanced metrics with Kähler fixed points

2018/05/02 by D. H. Phong, Sébastien Picard, Phong, Duong H. +3 · 4 citations
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1805.01029

openalex publication_date 2018/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

While the Anomaly flow was originally motivated by string theory, its zero slope case is potentially of considerable interest in non-Kahler geometry, as it is a flow of conformally balanced metrics whose stationary points are precisely Kahler metrics. We establish its convergence on Kahler manifolds for suitable initial data. We also discuss its relation to some current problems in complex geometry.

Citations

• Stable Forms, Vector Cross Products and Their Applications in Geometry
• (1,1) forms with specified Lagrangian phase: A priori estimates and\n algebraic obstructions
• The Anomaly flow and the Fu-Yau equation
• Positivity in convergence of the inverse σ_n-1-flow
• Fu-Yau Hessian Equations

Cited by

• A parabolic flow for the large volume heterotic G₂ system
• Flows of conformally coclosed G₂-structures with dilaton
• Positive Hermitian curvature flow on 2-step nilpotent Lie groups
• An introduction to conifold transitions

Related

• On the stability of the anomaly flow
• New curvature flows in complex geometry
• Anomaly flows
• Estimates for a geometric flow for the Type IIB string
• Tangent Flows of Kähler Metric Flows