New geometric flows on Riemannian manifolds and applications to Schrödinger-Airy flows |
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基金项目: | supported by National Natural Science Foundation of China(Grant Nos.11226082,11301557 and 10990013) |
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摘 要: | 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 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,the global results are obtained.
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关 键 词: | new geometric flow Schr¨odinger-Airy flow global existence |
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