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 |
All Science Journal Classification (ASJC) codes
- Geometry and Topology
Fingerprint Dive into the research topics of 'Binary differential equations at parabolic and umbilical points for 2-parameter families of surfaces'. Together they form a unique fingerprint.
Cite this
Deolindo-Silva, J. L., Kabata, Y., & Ohmoto, T. (2018). Binary differential equations at parabolic and umbilical points for 2-parameter families of surfaces. Topology and its Applications, 234, 457-473. https://doi.org/10.1016/j.topol.2017.11.014