We study the geometry of bifurcation sets of generic unfoldings of \(D_4^\pm \)-functions. Taking blow-ups, we show each of the bifurcation sets of \(D_4^\pm \)-functions admits a parametrization as a surface in \({\varvec{R}}^3\). Using this parametrization, we investigate the behavior of the Gaussian curvature and the principal curvatures. Furthermore, we investigate the number of ridge curves and subparabolic curves near their singular point.

中文翻译：

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柯兰克两个函数泛型展开的分岔集的几何

我们研究了\(D_4^\pm \)函数的泛型展开的分岔集的几何形状。进行放大，我们展示了\(D_4^\pm \)函数的每个分岔集都承认参数化为\({\varvec{R}}^3\) 中的表面。使用这种参数化，我们研究了高斯曲率和主曲率的行为。此外，我们研究了奇异点附近的脊曲线和亚抛物线曲线的数量。