  Some results about non-bijective quadratic transformations generalizing the
Kustaanheimo-Stiefel and the Levi-Civita transformations are reviewed in \S 1.
The three remaining sections are devoted to new results: \S 2 deals with the
Lie algebras under constraints associated to some Hurwitz transformations; \S 3
and \S 4 are concerned with several applications of some Hurwitz
transformations to wave equations for various potentials in $R^3$ and $R^5$.
