Geometric mean curvature lines on surfaces immersed in 𝐑 3
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 11 (2002) no. 3, pp. 377-401.
@article{AFST_2002_6_11_3_377_0,
     author = {Garcia, Ronaldo and Sotomayor, Jorge},
     title = {Geometric mean curvature lines on surfaces immersed in ${\bf R}^3$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {377--401},
     publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences},
     address = {Toulouse},
     volume = {Ser. 6, 11},
     number = {3},
     year = {2002},
     zbl = {02074272},
     mrnumber = {2015760},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2002_6_11_3_377_0/}
}
TY  - JOUR
AU  - Garcia, Ronaldo
AU  - Sotomayor, Jorge
TI  - Geometric mean curvature lines on surfaces immersed in ${\bf R}^3$
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2002
DA  - 2002///
SP  - 377
EP  - 401
VL  - Ser. 6, 11
IS  - 3
PB  - Université Paul Sabatier. Faculté des sciences
PP  - Toulouse
UR  - http://www.numdam.org/item/AFST_2002_6_11_3_377_0/
UR  - https://zbmath.org/?q=an%3A02074272
UR  - https://www.ams.org/mathscinet-getitem?mr=2015760
LA  - en
ID  - AFST_2002_6_11_3_377_0
ER  - 
Garcia, Ronaldo; Sotomayor, Jorge. Geometric mean curvature lines on surfaces immersed in ${\bf R}^3$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 11 (2002) no. 3, pp. 377-401. http://www.numdam.org/item/AFST_2002_6_11_3_377_0/

[1] Andronov (A.) and Leontovich (E.) et al. - Theory of Bifurcations of Dynamic Systems on a Plane, Jerusalem, Israel Program of Scientific Translations, 1973.

[2] Anosov (D.V.). - Geodesic Flows on Closed Riemannian Manifolds of Negative Curvature, Proc. Steklov Institute of Mathematics, Amer. Math. Soc. Transl., 90, 1967 and 1969. | MR 242194 | Zbl 0176.19101

[3] Banchoff (T.), Gaffney (T.) and Mccrory (C.). - Cusps of Gauss Maps, Pitman Research Notes in Math., London, 55 (1982), 1-130. | MR 657143 | Zbl 0478.53002

[4] Bruce (B.) and Fidal (D.). - On binary differential equations and umbilic points, Proc. Royal Soc. Edinburgh, 111A (1989), 147-168. | MR 985996 | Zbl 0685.34004

[5] Darboux (G.). - Leçons sur la Théorie des Surfaces, vol. IV. Sur la forme des lignes de courbure dans la voisinage d'un ombilic, Note 07, Paris:Gauthier Villars, 1896.

[6] Garcia (R.) and Sotomayor (J.). - Structural stability of parabolic points and periodic asymptotic lines, Matemática Contemporânea, 12 (1997), 83-102. | MR 1634428 | Zbl 0930.53003

[7] Garcia (R.) and Sotomayor (J.). - Structurally stable configurations of lines of mean curvature and umbilic points on surfaces immersed in R3, Publ. Matemátiques., 45:2 (2001), 431-466. | MR 1876916 | Zbl 1005.53003

[8] Garcia (R.) and Sotomayor (J.). - Lines of Harmonic Mean Curvature on surfaces immersed in R3, Pré-Publication du Laboratoire de Topologie, Université de Bourgogne, 294 (2002), 1-27. | MR 1992644

[9] Garcia (R.), Gutierrez (C.) and Sotomayor (J.). - Structural stability of asymptotic lines on surfaces immersed in R3, Bull. Sciences Math., 123 (1999), pp. 599-622. | MR 1725206

[10] Garcia (R.) and Sotomayor (J.). - Mean curvature lines on surfaces immersed in R3. In preparation.

[11] Guíñez (V.). - Positive quadratic differential forms and foliations with singularities on surfaces, Trans. Amer. Math. Soc., 309:2 (1988), pp. 477-502. | MR 961601 | Zbl 0707.57014

[12] Gutierrez (C.) and Sotomayor (J.). - Structural Stable Configurations of Lines of Principal Curvature, Asterisque, 98-99 (1982), 185-215. | MR 724448 | Zbl 0521.53003

[13] Gutierrez (C.) and Sotomayor (J.). - An Approximation Theorem for Immersions with Structurally Stable Configurations of Lines of Principal Curvature, Lect. Notes in Math., 1007, 1983. | MR 730276 | Zbl 0528.53002

[14] Gutierrez (C.) and Sotomayor (J.). - Lines of Curvature and Umbilic Points on Surfaces, 18th Brazilian Math. Colloquium, Rio de Janeiro, IMPA, 1991. Reprinted as Structurally Configurations of Lines of Curvature and Umbilic Points on Surfaces, Lima, Monografias del IMCA, 1998. | MR 2007065

[15] Gutierrez (C.) and Sotomayor (J.). - Lines of Curvature, Umbilical Points and Carathéodory Conjecture, Resenhas IME-USP, 03 (1998), 291-322. | MR 1633013 | Zbl 01696393

[16] Melo (W.) and Palis (J.). - Geometric Theory of Dynamical Systems, New York, Springer Verlag, 1982. | MR 669541 | Zbl 0491.58001

[17] Occhipinti (R.). - Sur un double système de lignes d'une surface. L'enseignement mathématique (1914), 38-44. | JFM 45.0874.01

[18] Ogura (K.). - On the T-System on a Surface, Tohoku Math. Journal, 09 (1916), 87-101. | JFM 46.1085.01

[19] Palis (J.) and Takens (F.). - Topological equivalence of normally hyperbolic dynamical systems, Topology, 16 (1977), 335-345. | MR 474409 | Zbl 0391.58015

[20] Peixoto (M.). - Structural Stability on two-dimensional manifolds, Topology, 1 (1962), 101-120. | MR 142859 | Zbl 0107.07103

[21] Roussarie (R.). - Bifurcations of Planar Vector Fields and Hilbert's Sixteen Problem, Progress in Mathematics, 164, Birkhaüser Verlag, Basel, 1988. | MR 1094374 | Zbl 0898.58039

[22] Spivak (M.). - Introduction to Comprehensive Differential Geometry, Vol. III Berkeley, Publish or Perish, 1980. | Zbl 0439.53003

[23] Sansone (G.) and Conti (R.). - Equazioni Differenziali non Lineari, Edizioni Cremonese, Roma, 1956. | MR 88607 | Zbl 0075.26803

[24] Struik (D.). - Lectures on Classical Differential Geometry, Addison Wesley Pub. Co., Reprinted by Dover Publications, Inc., 1988. | MR 939369 | Zbl 0697.53002