Gauss map of the skew mean curvature flow

Song, Chong

doi:10.1090/proc/13615

Gauss map of the skew mean curvature flow
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by Chong Song

Proc. Amer. Math. Soc. 145 (2017), 4963-4970

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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