TY - JOUR

T1 - Binary differential equations at parabolic and umbilical points for 2-parameter families of surfaces

AU - Deolindo-Silva, J. L.

AU - Kabata, Y.

AU - Ohmoto, T.

N1 - Funding Information:
The first and second authors thank organizers of the 14th Workshop on Real and Complex Singularities for giving them a nice opportunity to work together. The second author is supported by JSPS grant No. 16J02200. The third author is partly supported by JSPS grants No. 24340007 and 15K13452.
Publisher Copyright:
© 2017 Elsevier B.V.

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.

KW - Asymptotic curves

KW - Binary differential equations

KW - Flecnodal curve

KW - Parabolic curve

KW - Projective differential geometry of surfaces

KW - Singularities of smooth maps

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U2 - 10.1016/j.topol.2017.11.014

DO - 10.1016/j.topol.2017.11.014

M3 - Article

AN - SCOPUS:85040692568

SN - 0166-8641

VL - 234

SP - 457

EP - 473

JO - Topology and its Applications

JF - Topology and its Applications

ER -