Euclidean hypersurfaces with genuine conformal deformations in codimension two
Chion Aguirre, Sergio Julio
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We classify hypersurfaces f:Mn → Rn+1 with a principal curvature of multiplicity n − 2 that admit a genuine conformal deformation f':Mn → Rn+2. That a conformal deformation f':Mn → Rn+2 of f is genuine means that there does not exist any open subset U ⊂ M such that f'|U is a composition f'|U = h ◦ f|U of f|U with a conformal immersion h:V → Rn+2 of an open subset V ⊂ Rn+1 containing f(U).