A flow of conformally balanced metrics with Kähler fixed points

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.

34 pages; references added

References in corpus (5)

• Canonical metrics on holomorphic Courant algebroids
• The Anomaly flow over Riemann surfaces
• Fu-Yau Hessian Equations
• The inverse Monge-Ampere flow and applications to Kahler-Einstein metrics
• Stable Forms, Vector Cross Products and Their Applications in Geometry

Cited by in corpus (3)

• New curvature flows in complex geometry
• Parabolic complex Monge-Ampere equations on compact Kahler manifolds
• Parabolic complex Monge-Ampère equations on compact Hermitian manifolds