Geometric mean curvature lines on surfaces immersed in 𝐑 3
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 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},
     mrnumber = {2015760},
     zbl = {02074272},
     language = {en},
     url = {http://archive.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
SP  - 377
EP  - 401
VL  - 11
IS  - 3
PB  - Université Paul Sabatier. Faculté des sciences
PP  - Toulouse
UR  - http://archive.numdam.org/item/AFST_2002_6_11_3_377_0/
LA  - en
ID  - AFST_2002_6_11_3_377_0
ER  - 
%0 Journal Article
%A Garcia, Ronaldo
%A Sotomayor, Jorge
%T Geometric mean curvature lines on surfaces immersed in ${\bf R}^3$
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2002
%P 377-401
%V 11
%N 3
%I Université Paul Sabatier. Faculté des sciences
%C Toulouse
%U http://archive.numdam.org/item/AFST_2002_6_11_3_377_0/
%G en
%F AFST_2002_6_11_3_377_0
Garcia, Ronaldo; Sotomayor, Jorge. Geometric mean curvature lines on surfaces immersed in ${\bf R}^3$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 11 (2002) no. 3, pp. 377-401. http://archive.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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

[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

[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

[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 | Zbl

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

[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 | Zbl

[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

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

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

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

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

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

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

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

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

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

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