Some Geometric Flows on Kahler Manifolds

Abstract

We define a kind of KdV (Korteweg-de Vries) geometric flow for maps from a real line or a circle into a Kähler manifold (N, J,h) with complex structure J and metric h as the generalization of the vortex filament dynamics from a real line or a circle. By using the geometric analysis, the existence of the Cauchy problems of the KdV geometric flows will be investigated in this note.