Science China Mathematics

, Volume 57, Issue 11, pp 2247–2272 | Cite as

New geometric flows on Riemannian manifolds and applications to Schrödinger-Airy flows

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Abstract

In this paper, a class of new geometric flows on a complete Riemannian manifold is defined. The new flow is related to the generalized (third order) Landau-Lifshitz equation. On the other hand it could be thought of as a special case of the Schrödinger-Airy flow when the target manifold is a Kähler manifold with constant holomorphic sectional curvature. We show the local existence of the new flow on a complete Riemannian manifold with some assumptions on Ricci tensor. Moreover, if the target manifolds are Einstein or some certain type of locally symmetric spaces, the global results are obtained.

Keywords

new geometric flow Schrödinger-Airy flow global existence 

MSC(2010)

58J60 35Q53 
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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Statistics and MathematicsCentral University of Finance and EconomicsBeijingChina
  2. 2.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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