✦ LIBER ✦

Structural Stability of Asymptotic Lines on Surfaces Immersed in R3

✍ Scribed by R Garcia; C Gutierrez; J Sotomayor

Publisher: Elsevier Science
Year: 1999
Tongue: French
Weight: 254 KB
Volume: 123
Category: Article
ISSN: 0007-4497
DOI: 10.1016/s0007-4497(99)00116-5

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper are studied immersions of surfaces into to R 3 whose nets of asymptotic lines are topologically undisturbed under small perturbations of the immersion. These immersions are called structurally asymptotic stable. Sufficient conditions to belong to this class are established here. These conditions focus on the stable patterns around parabolic points, parabolic separatrix connections, periodic asymptotic lines (including those that intercept the parabolic lines) as well the exclusion of recurrent asymptotic lines. The class of immersions that are structurally stable in this sense is open in the C 5 -topology. © Éditions scientifiques et médicales Elsevier SAS

📜 SIMILAR VOLUMES

Harmonic mean curvature lines on surface

Harmonic mean curvature lines on surfaces immersed in( mathbb{R}^{3} )

✍ Ronaldo Garcia; Jorge Sotomayor 📂 Article 📅 2003 🏛 Springer 🌐 English ⚖ 270 KB

Lines of axial curvature on surfaces imm

Lines of axial curvature on surfaces immersed in R4

✍ Ronaldo Garcia; Jorge Sotomayor 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 135 KB

Lines of mean curvature on surfaces imme

Lines of mean curvature on surfaces immersed inR3

✍ Ronaldo Garcia; Jorge Sotomayor 📂 Article 📅 2004 🏛 SP Birkhäuser Verlag Basel 🌐 English ⚖ 413 KB

Lines of curvature near umbilical points

Lines of curvature near umbilical points on surfaces immersed in R4

✍ Federico Sánchez-Bringas; Ana Irene Ramírez-Galarza 📂 Article 📅 1995 🏛 Springer 🌐 English ⚖ 614 KB

Lines of curvature on surfaces immersed

Lines of curvature on surfaces immersed in ℝ4

✍ Carlos Gutierrez; Irwen Guadalupe; Renato Tribuzy; Víctor Guíñez 📂 Article 📅 1997 🏛 Springer 🌐 English ⚖ 696 KB

Umbilicity of surfaces with orthogonal a

Umbilicity of surfaces with orthogonal asymptotic lines in R4

✍ Marı́a del Carmen Romero-Fuster; Federico Sánchez-Bringas 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 103 KB

We study some properties of surfaces in 4-space all whose points are umbilic with respect to some normal field. In particular, we show that this condition is equivalent to the orthogonality of the (globally defined) fields of asymptotic directions. We also analyze necessary and sufficient conditions