Lines of curvature and umbilic points on surfaces

Jorge Sotomayor

Séminaire de théorie spectrale et géométrie (1991-1992)

  • Volume: 10, page 9-12
  • ISSN: 1624-5458

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Sotomayor, Jorge. "Lines of curvature and umbilic points on surfaces." Séminaire de théorie spectrale et géométrie 10 (1991-1992): 9-12. <http://eudml.org/doc/114331>.

@article{Sotomayor1991-1992,
author = {Sotomayor, Jorge},
journal = {Séminaire de théorie spectrale et géométrie},
language = {eng},
pages = {9-12},
publisher = {Institut Fourier},
title = {Lines of curvature and umbilic points on surfaces},
url = {http://eudml.org/doc/114331},
volume = {10},
year = {1991-1992},
}

TY - JOUR
AU - Sotomayor, Jorge
TI - Lines of curvature and umbilic points on surfaces
JO - Séminaire de théorie spectrale et géométrie
PY - 1991-1992
PB - Institut Fourier
VL - 10
SP - 9
EP - 12
LA - eng
UR - http://eudml.org/doc/114331
ER -

References

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  1. [Da] DARBOUX G. - Sur la forme des lignes de courbure dans le voisinage d'un ombilic, Leçons sur la théorie des surfaces, IV, Note 7, Gauthier Villars, Paris, 1896. Zbl34.0655.01
  2. [Fi] FISCHER G. - Mathematical Models, Vieweg, 1986. MR851014
  3. [H-CV] HILBERT D., COHN VOSSEN S. - Geometry and the Imagination, Chelsea, 1952. Zbl0047.38806MR46650
  4. [Ga] GARCIA R. - Linhas de curvatura de hipersuperficies imersas no espaço R4, Thesis 1989; Preprint IMPA, F-027/89. See also : Anais da Acad; Bras. Ciencias, 64, 1, 1992. 
  5. [Ga-S,l] GARCIA R. , SOTOMAYOR J. - Lines of curvature near singular points of implicit surfaces, To appear in Bulletin des Sciences Mathématiques. Zbl0791.53007MR1228948
  6. [Ga-S,2] GARCIA R. , SOTOMAYOR J. - Lines of curvature near principal cycles, Annals of global analysis and geometry, 10, 3, 1992. Zbl0768.53002MR1186016
  7. [G-S,l] GUTIERREZ C , SOTOMAYOR J. - Structurally stable configurations of lines of principal curvature, Astérisque, 98-99, 1982. Zbl0521.53003MR724448
  8. [G-S,2] GUTIERREZ C , SOTOMAYOR J. - An approximation theorem for immersions with structurally stable configurations of lines of principal curvature, Springer Lect. Notes in Math., 1007, 1983. Zbl0528.53002MR730276
  9. [G-S,3] GUTIERREZ C , SOTOMAYOR J. - Lines of curvature on surfaces immers ed with constant mean curvature, Trans. Amer. Math. Soc.,232, 2, 1986. Zbl0598.53007MR816323
  10. [G-S,4] GUTIERREZ C, SOTOMAYOR J. - Lines of principal curvature on surfaces with Whitney umbrella singularities, Tôhoku Mathematical Journal, 38, 4, 1986. Zbl0611.53007MR867061
  11. [G-S,5] GUTIERREZ C, SOTOMAYOR J. - Closed lines of curvature and bifurcation, Bolet. Soc. Bras. Mat., 17, 1986. Zbl0608.53003MR869705
  12. [G-S,6] GUTIERREZ C, SOTOMAYOR J. - Periodic lines of curvature bifurcating from Darbouxian umbilic connections, Springer Lect. Notes on Math.,1455, 1991. Zbl0714.34057MR1094381
  13. [G-S,7] GUTIERREZ C, SOTOMAYOR J. - Configurations of principal lines of curvature and their bifurcations, Aportaciones Matemáticas, Soc. Mat. de México, Notas de Investigacion, n° l , 1985. Zbl0587.58026MR823707
  14. [G-S,8] GUTIERREZ C, SOTOMAYOR J. - Lines of curvature and ombilic points on surfaces, Text of course delivered at the 18th Brazilian Math. Colloquium, IMPA, 1991. 
  15. [G-S,9] GUTIERREZ C, SOTOMAYOR J. - Bifurcations of umbilic points and related principal cycles, Preprint, IMPA, 1992. Zbl1075.53004
  16. [G-S, et al] GUTIERREZ C, SOTOMAYOR J., GUADALUPE I., TRIBUZY R. - Lines of curvature on surfaces minimally immersed on constantly curved 4-spaces, Pitman Res., Notes in Math. Series, 160, Longman, 1987. Zbl0633.53010
  17. [M] MONGE G. - Sur les lignes de courbure de la surface de l'ellipsoïde, Journ. de l'Ecole Polytechnique, IIe cah., 1796. 
  18. [S] SOTOMAYOR J. - Closed principal lines for Weingarten immersions, Annals of Global Analysis and Geometry, 5, 1, 1987. Zbl0638.05035MR933908

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