| Abstract: |
A submersion between two Riemannian manifolds is said to be
semiconformal if it is conformal orthogonal to the fibres. Joint work with
Paul Baird produces many examples semiconformal mappings from Euclidean
3-space to Euclidean 2-space and, under mild non-degeneracy assumptions,
gives necessary and sufficient conditions in order that a function on
3-space be one of the components of such a mapping. These conditions are in
the form of non-linear partial differential equations. They may also be
regarded as conformal invariants of a smooth function. As such, some of
these invariants have interesting geometric significance. Nothing much will
be assumed of the audience and all terminology will be explained from
scratch.
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