The analogue of Wilczynski's projective frame in Lie sphere geometry: Lie-applicable surfaces and commuting Schr\"odinger operators with magnetic fields
Abstract
We propose a twistor construction of surfaces in Lie sphere geometry based on the linear system which copies equations of Wilczynski's projective frame. In the particular case of Lie-applicable surfaces this linear system describes joint eigenfunctions of a pair of commuting Schr\"odinger operators with magnetic fields.
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