2015-02-052014-09-29DIAS , D. G. Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano. 2014. 68 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2014.http://repositorio.bc.ufg.br/tede/handle/tede/4091We present hypersurfaces with prescribed normal Gauss map. These surfaces are obtained as the envelope of a sphere congruence where the other envelope is contained in a plane. We introduce classes of surfaces that generalize linear Weingarten surfaces, where the coefficients are functions that depend on the support function and the distance function from a fixed point (in short, DSGW-surfaces). The linear Weingarten surfaces, the Appell’s surfaces and the Tzitzeica’s surfaces are all DSGW-surfaces. From them we obtain new classes of DSGW-surfaces applying inversions and dilatations. For a special class of DSGW-surfaces, which is invariant under dilatations and inversions, we obtain a Weierstrass type representation (in short, EDSGW-surfaces). As application we classify the EDSGW-surfaces of rotation and present a 4-parameter family of complete cyclic EDSGW-surfaces with an isolated singularity and foliated by non-parallel planes. We generalized the EDSGW-surfaces for the case of hypersurfaces in Rn+1, n ≥ 2. We present a representation for these hypersurfaces in the case where the stereographic projection of the normal Gauss map N is given by the identity application. As an application, we will characterize the rotational examples.application/pdfAcesso AbertoSuperfícies Weingarten generalizadaRepresentação tipo WeierstrassAplicação normal de Gauss prescritaGeneralized Weingarten surfacesWeierstrass type representationPrescribed normal Gauss mapALGEBRA::GEOMETRIA ALGEBRICATese