Volume 111 / 2014
Annales Polonici Mathematici 111 (2014), 107-135 MSC: 53A15, 53A07, 53B25, 53C42. DOI: 10.4064/ap111-2-1
We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.