For hypersurfaces of spheres, the Gauss map into the complex quadric is Lagrangian, and principal curvatures are the cotangent of local angle functions; the local converse is constructed explicitly.
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Lagrangian submanifolds of the complex quadric as Gauss maps of hypersurfaces of spheres
For hypersurfaces of spheres, the Gauss map into the complex quadric is Lagrangian, and principal curvatures are the cotangent of local angle functions; the local converse is constructed explicitly.