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arXiv · 1305.2774

New Geometric Flows on Riemannian Manifolds and Applications to Schr\"odinger-Airy Flows

Xiaowei Sun·Youde Wang
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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 Schr\"odinger-Airy flow when the target manifold is a K\"ahler 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.

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Xiaowei Sun, Youde Wang. 2013-05-13. New Geometric Flows on Riemannian Manifolds and Applications to Schr\"odinger-Airy Flows. https://arxiv.org/abs/1305.2774

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