Binary differential equations at parabolic and umbilical points for 2-parameter families of surfaces
Binary differential equations at parabolic and umbilical points for 2-parameter families of surfaces
复制标题
2 参数曲面族的抛物线点和脐点处的二元微分方程
DOI：
10.1016/j.topol.2017.11.014
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发表时间：
2018
影响因子：
0.6
通讯作者：
Ohmoto T.
中科院分区：
文献类型：
--
作者：
Deolindo-Silva J.L.;Kabata Y.;Ohmoto T.
通过比较我们对Monge型的射影分类和Tari和奥利弗对一般BDE的分类，确定了P3中一般2-参数曲面族在抛物和平坦脐点处的渐近曲线的二元微分方程的局部拓扑类型.特别是，一般的抛物曲线的分叉进行了分类。通过直接计算，我们还研究了屈曲节点曲线，并在典型例子中给出了新的分叉图。
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 P 3 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.