@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://proceedings.centre-mersenne.org/articles/10.5802/tsg.95/} }
TY - JOUR AU - Jorge Sotomayor TI - Lines of curvature and umbilic points on surfaces JO - Séminaire de théorie spectrale et géométrie PY - 1991-1992 SP - 9 EP - 12 VL - 10 PB - Institut Fourier PP - Grenoble UR - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.95/ DO - 10.5802/tsg.95 LA - en ID - TSG_1991-1992__10__9_0 ER -
%0 Journal Article %A Jorge Sotomayor %T Lines of curvature and umbilic points on surfaces %J Séminaire de théorie spectrale et géométrie %D 1991-1992 %P 9-12 %V 10 %I Institut Fourier %C Grenoble %U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.95/ %R 10.5802/tsg.95 %G en %F TSG_1991-1992__10__9_0
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://proceedings.centre-mersenne.org/articles/10.5802/tsg.95/
[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
[H-CV] Hilbert D., Cohn Vossen S. - Geometry and the Imagination, Chelsea, 1952. | MR | Zbl
[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 | Zbl
[Ga-S,2] Garcia R. , Sotomayor J. - Lines of curvature near principal cycles, Annals of global analysis and geometry, 10, 3, 1992. | MR | Zbl
[G-S,l] Gutierrez C , Sotomayor J. - Structurally stable configurations of lines of principal curvature, Astérisque, 98-99, 1982. | MR | Zbl
[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 | Zbl
[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 | Zbl
[G-S,4] Gutierrez C, Sotomayor J. - Lines of principal curvature on surfaces with Whitney umbrella singularities, Tôhoku Mathematical Journal, 38, 4, 1986. | MR | Zbl
[G-S,5] Gutierrez C, Sotomayor J. - Closed lines of curvature and bifurcation, Bolet. Soc. Bras. Mat., 17, 1986. | MR | Zbl
[G-S,6] Gutierrez C, Sotomayor J. - Periodic lines of curvature bifurcating from Darbouxian umbilic connections, Springer Lect. Notes on Math.,1455, 1991. | MR | Zbl
[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 | Zbl
[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
[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
[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 | Zbl
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