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Lines of curvature and umbilic points on surfaces
Jorge Sotomayor
Séminaire de théorie spectrale et géométrie, Volume 10 (1991-1992), pp. 9-12.
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MR: 1715907
DOI: 10.5802/tsg.95
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@article{TSG_1991-1992__10__9_0,
     author = {Jorge Sotomayor},
     title = {Lines of curvature and umbilic points on surfaces},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {9--12},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {10},
     year = {1991-1992},
     doi = {10.5802/tsg.95},
     mrnumber = {1715907},
     language = {en},
     url = {https://tsg.centre-mersenne.org/articles/10.5802/tsg.95/}
}
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Jorge Sotomayor. Lines of curvature and umbilic points on surfaces. Séminaire de théorie spectrale et géométrie, Volume 10 (1991-1992), pp. 9-12. doi : 10.5802/tsg.95. https://tsg.centre-mersenne.org/articles/10.5802/tsg.95/
  • References
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[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.

[Fi] Fischer G. - Mathematical Models, Vieweg, 1986. | MR: 851014

[H-CV] Hilbert D., Cohn Vossen S. - Geometry and the Imagination, Chelsea, 1952. | MR: 46650 | Zbl: 0047.38806

[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.

[Ga-S,l] Garcia R. , Sotomayor J. - Lines of curvature near singular points of implicit surfaces, To appear in Bulletin des Sciences Mathématiques. | MR: 1228948 | Zbl: 0791.53007

[Ga-S,2] Garcia R. , Sotomayor J. - Lines of curvature near principal cycles, Annals of global analysis and geometry, 10, 3, 1992. | MR: 1186016 | Zbl: 0768.53002

[G-S,l] Gutierrez C , Sotomayor J. - Structurally stable configurations of lines of principal curvature, Astérisque, 98-99, 1982. | MR: 724448 | Zbl: 0521.53003

[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. | MR: 730276 | Zbl: 0528.53002

[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. | MR: 816323 | Zbl: 0598.53007

[G-S,4] Gutierrez C, Sotomayor J. - Lines of principal curvature on surfaces with Whitney umbrella singularities, Tôhoku Mathematical Journal, 38, 4, 1986. | MR: 867061 | Zbl: 0611.53007

[G-S,5] Gutierrez C, Sotomayor J. - Closed lines of curvature and bifurcation, Bolet. Soc. Bras. Mat., 17, 1986. | MR: 869705 | Zbl: 0608.53003

[G-S,6] Gutierrez C, Sotomayor J. - Periodic lines of curvature bifurcating from Darbouxian umbilic connections, Springer Lect. Notes on Math.,1455, 1991. | MR: 1094381 | Zbl: 0714.34057

[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. | MR: 823707 | Zbl: 0587.58026

[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.

[G-S,9] Gutierrez C, Sotomayor J. - Bifurcations of umbilic points and related principal cycles, Preprint, IMPA, 1992. | Zbl: 1075.53004

[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. | Zbl: 0633.53010

[M] Monge G. - Sur les lignes de courbure de la surface de l'ellipsoïde, Journ. de l'Ecole Polytechnique, IIe cah., 1796.

[S] Sotomayor J. - Closed principal lines for Weingarten immersions, Annals of Global Analysis and Geometry, 5, 1, 1987. | MR: 933908 | Zbl: 0638.05035

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