K-isothermic hypersurfaces
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Data
2020-07-25
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Editor
Universidade Federal de Goiás
Resumo
We 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.
Descrição
Palavras-chave
k-isothermic hypersurfaces, Dupin hypersurfaces, Irreducible hyper- surface, Hipersuperfície k-isotérmica, Hipersuperfície de Dupin, Hipersuperfícies irredutível
Citação
V. 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.