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Gauss map of the skew mean curvature flow


Author: Chong Song
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 53C44, 76B47, 35Q55
DOI: https://doi.org/10.1090/proc/13615
Published electronically: May 30, 2017
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Abstract: The skew mean curvature flow (SMCF) is a natural generalization of the famous vortex filament equation. In this note, we show that the Gauss map of the SMCF satisfies a Schrödinger flow equation. In this regard, we explore the geometry of the oriented Grassmannian manifold explicitly by embedding it into the exterior product space.


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Additional Information

Chong Song
Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China
Email: songchong@xmu.edu.cn

DOI: https://doi.org/10.1090/proc/13615
Received by editor(s): June 5, 2016
Received by editor(s) in revised form: December 9, 2016
Published electronically: May 30, 2017
Communicated by: Lei Ni
Article copyright: © Copyright 2017 American Mathematical Society