Stable Plane-Gauss Maps on Closed Orientable Surfaces

C. M. de Jesus, P. D. Romero, L. J. Santos



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.


Closed surfaces, graphs, stable maps

Full Text:



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$sim$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/

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


Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)


Indexed in:




Desenvolvido por:

Logomarca da Lepidus Tecnologia