Gauss map of the skew mean curvature flow

TL;DR

This paper investigates the geometric properties of the skew mean curvature flow by showing its Gauss map satisfies a Schrödinger flow, linking curvature flow with complex geometric evolution.

Contribution

It demonstrates that the Gauss map of the SMCF obeys a Schrödinger flow equation and explores the geometry of the Grassmannian manifold explicitly.

Findings

Gauss map of SMCF satisfies a Schrödinger flow

Explicit embedding of Grassmannian manifold into exterior product space

Provides geometric insights into curvature flow dynamics

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 Schr\"odinger flow equation. In this regard, we explore the geometry of the oriented Grassmannian manifold explicitly by embedding it into the exterior product space.