Local Nonautonomous Schr\"{o}dinger Flows on K\"{a}hler Manifolds

TL;DR

This paper proves the existence and uniqueness of local solutions for nonautonomous Schrödinger flows from compact Riemannian manifolds into Kähler manifolds, with higher regularity under certain conditions.

Contribution

It establishes the local existence, uniqueness, and regularity results for nonautonomous Schrödinger flows into Kähler manifolds, extending previous understanding in geometric analysis.

Findings

Local solutions exist for the nonautonomous Schrödinger flow.

Solutions are unique under certain conditions.

Solutions possess higher regularity when specific criteria are met.

Abstract

$\,\,\,\,\,\,$In this paper, we prove that the nonautonomous Schr\"{o}dinger flow from a compact Riemannian manifold into a K\"ahler manifold admits a local solution. Under some certain conditions, the solution is unique and has higher regularity.