The analogue of Wilczynski's projective frame in Lie sphere geometry: Lie-applicable surfaces and commuting Schrödinger operators with magnetic fields

Details The analogue of Wilczynski's projective frame in Lie sphere geometry: Lie-applicable surfaces and commuting Schrödinger operators with magnetic fields The analogue of Wilczynski's projective frame in Lie sphere geometry: Lie-applicable surfaces and commuting Schrödinger operators with magnetic fields

2001-04-03

arxiv.org/abs/math/0104034v1

Mathematics

Differential Geometry

25 pages, Latex

Scientific paper

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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