“Generalized cubic curves” were introduced in Costantini and Manni (2006) as a special case of the more general results in Goodman and Mazure (2001) and Costantini, Lyche and Manni (2005). In this work, the shape of these curves is analyzed in ${\mathbb{R}}^n$, $n=1,2,3$, proving that well-known theorems, which hold for cubic polynomials, hold also for this class of curves.

中文翻译：

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广义三次曲线的形状分析

Costantini和Manni（2006）中引入了“广义三次曲线”，作为Goodman和Mazure（2001）和Costantini，Lyche和Manni（2005）中更一般性结果的特例。在这项工作中，这些曲线的形状在${\mathbb{[R}}^{ñ}$， $ñ=\mathrm{1个}，2，3$证明了适用于三次多项式的著名定理也适用于此类曲线。