Use este identificador para citar ou linkar para este item: 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
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