Stable Plane-Gauss Maps on Closed Orientable Surfaces

Autores

DOI:

https://doi.org/10.5540/tcam.2023.024.02.00305

Palavras-chave:

Closed surfaces, graphs, stable maps

Resumo

 

The aim of this paper is to study the couple of stable plane Gauss maps f = (f2, f3): M→ R^2×S^2 from a global point of view, where M is a smooth closed orientable surface, f2 is a projection and f3 is Gauss map. We associate this maps a pair of MF-graph. We will study their properties, giving conditions on the graphs that can be realized by pairs of maps with couples from pre-determined singular sets.

Biografia do Autor

C. M. de Jesus, Universidade Federal de Juiz de Fora

Departamento de Matemática, ICE

P. D. Romero, Universidad Cardenal Herrera-CEU

Matemática, Matemática Aplicada

L. J. Santos, Universidade Federal de Juiz de Fora

Matemática, Geometria e Topologia

Referências

V. I. Arnol'd, S. M. Gusein-Zade and A. N. Varchenko, textit{Singularities of differentiable maps. Vol. I. The classification of critical points, caustics and wave fronts}, textit{Translated from the Russian by Ian Porteous and Mark Reynolds}. Monographs in Mathematics, 82. Birkhäuser Boston, Inc., Boston, MA, (1985).

T. Banchoff, T. Gaffney and C. McCrory, textit{Cusps of Gauss Mappings}, {Pitman Books Limited}, London, (1982). Web version with D. Dreibelbis www.math.brown.edu/$sim$dan/cgm/index.html

J. W. Bruce, P. J. Giblin and F. Tari, textit{Families of surfaces: height functions, Gauss maps and duals}, Real and Complex Singularities, ed. W. L. Marar, {Pitman Research Notes in Mathematics}, 333 (1995), 148--178.

M. Golubitsky and V. Guillemin, textit{Stable Mappings and Their Singularities}, Springer Verlag, Berlin (1976).

D. Hacon, C. Mendes de Jesus and M. C. Romero Fuster, textit{Stable maps from surfaces to the plane with prescribed branching data}, {Topology and Its Appl.} 154 (1) (2007), 166--175. DOI:10.1016/j.topol.2006.04.005.

C. Mendes de Jesus, S. M. de Moraes and M. C. Romero Fuster, textit{Stable Gauss maps on surfaces from a global viewpoint}, {Bulletin of the Brazilian Mathematical Society}, 42 (2011), 87--103. DOI: 10.1007/s00574-011-0005-8

T. Ohmoto and F. Aicardi, textit{First order local invariants of apparent contours}. Topology, 45 (2006), 27--45. DOI:10.1016/j.top.2005.04.005.

M. C. Romero Fuster, textit{Sphere stratifications and the Gauss map}, {Proceedings of the Royal Society of Edinburgh}, 95A (1983), 115--136. DOI:10.1017/S0308210500015821

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Publicado

2023-05-24

Como Citar

de Jesus, C. M., Romero, P. D., & Santos, L. J. (2023). Stable Plane-Gauss Maps on Closed Orientable Surfaces. Trends in Computational and Applied Mathematics, 24(2), 305–318. https://doi.org/10.5540/tcam.2023.024.02.00305

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Seção

Artigo Original