Structurally stable configurations of lines of mean curvature and umbilic points on surfaces immersed in R3.

Título inglés Structurally stable configurations of lines of mean curvature and umbilic points on surfaces immersed in R3.
Título español Configuraciones estructuralmente estables de líneas de curvatura media y puntos umbilicales en superficies inmersas en R3.
Autor/es García, Ronaldo ; Sotomayor, Jorge
Organización Inst. Mat. Estatíst. Univ. Fed. Goiás, Goiânia (Goiás), Brasil;Inst. Mat. Estatíst. Univ. Sao Paulo, Sao Paulo, Brasil
Revista 0214-1493
Publicación 2001, 45 (2): 431-466, 20 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés In this paper we study the pairs of orthogonal foliations on oriented surfaces immersed in R3 whose singularities and leaves are, respectively, the umbilic points and the lines of normal mean curvature of the immersion. Along these lines the immersions bend in R3 according to their normal mean curvature. By analogy with the closely related Principal Curvature Configurations studied in [S-G], [GS2], whose lines produce the extremal normal curvature for the immersion, the pair of foliations by lines of normal mean curvature and umbilics, assembled together, are called Mean Curvature Configurations. This paper studies the stable and generic cases of umbilic points and mean curvature cycles, with their Poincaré map. This provides two of the essential local ingredients to establish sufficient conditions for mean curvature structural stability, the analog of principal curvature structural stability, [S-G], [GS2].
Clasificación UNESCO 120404
Palabras clave español Geometría euclídea ; Superficies ; Curvatura
Código MathReviews MR1876916
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