Harmonic maps in unfashionable geometries

Abstract

We describe some general constructions on a real smooth projective 4-quadric which provide analogues of the Willmore functional and conformal Gauss map in both Lie sphere and projective differential geometry. Extrema of these functionals are characterized by harmonicity of this Gauss map.

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Cited by in corpus (11)

• On organizing principles of Discrete Differential Geometry. Geometry of spheres
• Equivariant harmonic cylinders
• Adjoint Transform of Willmore Surfaces in $n$-sphere
• Lie applicable surfaces
• Notes on transformations in integrable geometry
• Constant mean curvature surfaces in hyperbolic 3-space via loop groups
• The Gauss maps of Demoulin surfaces with conformal coordinates
• G-Deformations of maps into projective space
• Conformal geometry of quasi-umbilical timelike surfaces
• A loop group method for Demoulin surfaces in the 3-dimensional real projective space
• Tableaux over Lie algebras, integrable systems, and classical surface theory