Local Schrödinger flow into Kähler manifolds

• Published in: Science China. Mathematics Vol. 44; no. 11; pp. 1446 - 1464
• Main Authors: Ding, Weiyue, Wang, Youde
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.11.2001
• Subjects: Cauchy problems; Euclidean geometry; Flow mapping; Riemann manifold; Sobolev space

In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrödinger flow for maps from a compact Riemannian manifold into a complete Kähler manifold, or from a Euclidean space Rm into a compact Kähler manifold. As a consequence, we prove that Heisenberg s...