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https://locus.ufv.br//handle/123456789/21723
Tipo: | Artigo |
Título: | Envelope of Mid-Planes of a surface and some classical notions of affine differential geometry |
Autor(es): | Cambraia Jr., Ady Craize, Marcos |
Abstract: | For a pair of points in a smooth locally convex surface in 3-space, its mid-plane is the plane containing its mid-point and the intersection line of the corresponding pair of tangent planes. In this paper we show that the limit of mid-planes when one point tends to the other along a direction is the Transon plane of the direction. Moreover, the limit of the envelope of mid-planes is non-empty for at most six directions, and, in this case, it coincides with the center of the Moutard’s quadric. These results establish a connection between these classical notions of affine differential geometry and the apparently unrelated concept of envelope of mid-planes of a surface. We call the limit of envelope of mid-planes the affine mid-planes evolute and prove that, under some generic conditions, it is a regular surface in 3-space. |
Palavras-chave: | Transon planes Cone of B.Su Moutard’s quadrics Affine evolute |
Editor: | Results in Mathematics |
Tipo de Acesso: | Springer Science+Business Media, LLC, part of Springer Nature |
URI: | https://doi.org/10.1007/s00025-017-0697-1 http://www.locus.ufv.br/handle/123456789/21723 |
Data do documento: | 26-Mai-2017 |
Aparece nas coleções: | Artigos |
Arquivos associados a este item:
Arquivo | Descrição | Tamanho | Formato | |
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artigo.pdf Until 2100-12-31 | Texto completo | 511,1 kB | Adobe PDF | Visualizar/Abrir ACESSO RESTRITO |
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