K\"ahler stability of symplectic forms
Jeffrey Streets, Gang Tian
TL;DR
This paper demonstrates that on compact Calabi-Yau manifolds, small symplectic deformations of a K"ahler form preserve the K"ahler property, using dynamical stability of symplectic curvature flow.
Contribution
It introduces a new stability result for K"ahler forms under symplectic deformations on Calabi-Yau manifolds via symplectic curvature flow.
Findings
Small symplectic deformations remain K"ahler
Dynamical stability of symplectic curvature flow is effective
Preservation of K"ahler condition under deformation
Abstract
Using dynamical stability of symplectic curvature flow, we show that on a compact Calabi-Yau manifold, any small symplectic deformation of a K\"ahler form remains K\"ahler.
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Taxonomy
TopicsGeometry and complex manifolds · Black Holes and Theoretical Physics · Homotopy and Cohomology in Algebraic Topology