Abstract
We determine local topological types of binary differential equations of asymptotic curves at parabolic and flat umbilical points for generic 2-parameter families of surfaces in P3 by comparing our projective classification of Monge forms and classification of general BDE obtained by Tari and Oliver. In particular, generic bifurcations of the parabolic curve are classified. The flecnodal curve is also examined by direct computations, and we present new bifurcation diagrams in typical examples.
| Original language | English |
|---|---|
| Pages (from-to) | 457-473 |
| Number of pages | 17 |
| Journal | Topology and its Applications |
| Volume | 234 |
| DOIs | |
| Publication status | Published - Feb 1 2018 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Geometry and Topology
Cite this
Binary differential equations at parabolic and umbilical points for 2-parameter families of surfaces. / Deolindo-Silva, J. L.; Kabata, Yutaro; Ohmoto, T.
In: Topology and its Applications, Vol. 234, 01.02.2018, p. 457-473.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Binary differential equations at parabolic and umbilical points for 2-parameter families of surfaces
AU - Deolindo-Silva, J. L.
AU - Kabata, Yutaro
AU - Ohmoto, T.
PY - 2018/2/1
Y1 - 2018/2/1
N2 - We determine local topological types of binary differential equations of asymptotic curves at parabolic and flat umbilical points for generic 2-parameter families of surfaces in P3 by comparing our projective classification of Monge forms and classification of general BDE obtained by Tari and Oliver. In particular, generic bifurcations of the parabolic curve are classified. The flecnodal curve is also examined by direct computations, and we present new bifurcation diagrams in typical examples.
AB - We determine local topological types of binary differential equations of asymptotic curves at parabolic and flat umbilical points for generic 2-parameter families of surfaces in P3 by comparing our projective classification of Monge forms and classification of general BDE obtained by Tari and Oliver. In particular, generic bifurcations of the parabolic curve are classified. The flecnodal curve is also examined by direct computations, and we present new bifurcation diagrams in typical examples.
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UR - http://www.scopus.com/inward/citedby.url?scp=85040692568&partnerID=8YFLogxK
U2 - 10.1016/j.topol.2017.11.014
DO - 10.1016/j.topol.2017.11.014
M3 - Article
AN - SCOPUS:85040692568
VL - 234
SP - 457
EP - 473
JO - Topology and its Applications
JF - Topology and its Applications
SN - 0166-8641
ER -