New Geometric Flows on Riemannian Manifolds and Applications to Schrödinger-Airy Flows

Abstract

In this paper, we define a class of new geometric flows on a complete Riemannian manifold. The new flow is related to the generalized (third order) Landau-Lifishitz equation. On the other hand it could be thought of 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, we obtain the global results.

33 pages. arXiv admin note: substantial text overlap with arXiv:1203.0549