2022-03-152022-03-152020-07-25V. CORRO, Armando M.; RODRIGUES, Luciana Ávila; FERRO, Marcelo Lopes. K-isothermic Hypersurfaces. NEXUS Mathematicæ, Goiânia, v. 3, e20004, 2020.Disponível em: https://www.revistas.ufg.br/nexus/article/view/60657.2595-9824http://repositorio.bc.ufg.br/handle/ri/20373We consider n dimensional hypersurfaces in the Euclidean space and introduce the k-isothermic hypersurfaces, with k < n, as hypersurfaces that locally admit orthogonal parametrization by curvature lines with k distinct coefficients of the first fundamental form. It easy to check that the transformations: isometries, dilations and invertions, preserve k-isothermic hypersurfaces. We prove that there are no k-isothermic hypersurface of dimension n with distinct principal curvatures for n ≥ k + 3. We introduced two ways to generate a (k + 1)-isothermic hypersurface from a k-isothermic hypersurfaces, which we will call 2-reducible. Moreover, we provide a local characterization of Dupin 2-isothermic hypersurfaces and include explicit examples of 2-irreducible Dupin 2-isothermic hypersurfaces.engAcesso Abertok-isothermic hypersurfacesDupin hypersurfacesIrreducible hyper- surfaceHipersuperfície k-isotérmicaHipersuperfície de DupinHipersuperfícies irredutívelArtigo10.5216/nm.v3.60657