2019-04-252019-04-02SANTOS, L. R. P. Uma classe de hipersuperfícies Weingarten generalizada associadas a esfera. 2019. 110 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019.http://repositorio.bc.ufg.br/tede/handle/tede/9535In this work we study a particular class of WGSD surfaces called generalized Weingarten of the radial support type – WGSR surfaces – which satisfy a differentiable relation between the mean and Gaussian curvatures, the support function and the radius function associated with a sphere congruence. They are obtained locally as envelopes of a sphere congruence whose other envelope is a unit sphere. We characterize these surfaces in terms of a harmonic function and we provide a Weierstrass type representation depending on two holomorphic functions.application/pdfAcesso AbertoSuperfícies Weingarten generalizadaRepresentação tipo WeierstrassFunção holomorfaFunção harmônicaGeneralized Weingarten surfacesWeierstrass type representationHolomorphic functionHarmonic functionCIENCIAS EXATAS E DA TERRA::MATEMATICATese