Grahps of stable plane-Gauss maps

Catarina Mendes de Jesus, Laércio José dos Santos, Pantaleón D. Romero


In this paper, we present immersions of a given closed and oriented surface M in R3, where the two applications are stable: projection on the plane xy and a Gauss map. The projection  on the plane can be seen as a stable map of surfaces on the plane.


Closed sufarces; Graphs; stable maps

Texto completo:

PDF (English)


ArnoFd, V. I., Gusein-Zade, S. M. and Varchenko, A. N. Singularities of differentiable maps. Vol. I. The classification of criticai points, caustics and wave fronts, Translated from the Russian by Ian Porteous and Mark Reynolds, Monographs in Mathematics, 82. Birkhãuser Boston, Inc., Boston, MA, 1985.

Banchoff, T., Gaffney, T. and McCrory, C. Cusps of Gauss Mappings, Pitman Books Limited, London, 1982.

Bruce,J. W., Giblin, P. J. and Tari, F. Families of surfaces: height functions, Gauss maps and duais, Real and Complex Singularities, ed. W. L. Marar, Pitman Research Notes in Mathematics, volume 333, pages 148-178, 1995.

Golubitsky, M. and Guillemin, V. Stable Mappings and Their Singularities, Springer Verlag, Berlin, 1976.

Hacon, D., Mendes de Jesus, C. and Romero-Fuster, M.C. Topological invariants of stable maps from a surface to the plane from a global viewpoint, Real and Complex Singularities, in: Lecture Notes in Pure and Appl. Math, Dekker, New York,, volume 232, pages 227-235, 2003. DOLIO.1201/9780203912089.

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

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

Ohmoto, T. and Aicardi, F. First order local invariants of apparent contours. Topology, volume 45, chapter 23, pages 27-45, 2006. DOI: 10.1016/

Romero-Fuster, M. C. Sphere stratifications and the Gauss map, Proceedings of the Royal Society of Edinburgh, volume 95, pages 115-136, 1983. DOI: 10.1017/S0308210500015821.



  • Não há apontamentos.

SBMAC - Sociedade de Matemática Aplicada e Computacional
Edifício Medical Center - Rua Maestro João Seppe, nº. 900, 16º. andar - Sala 163 | São Carlos/SP - CEP: 13561-120

Normas para publicação | Contato