We consider a variational problem of $p$-elastic curves in two-dimensional sphere. We give its first variation formula, and in two-dimensional sphere, we give a realization of a solution which satisfies that the first variation formula is zero. We also show the existence of a flat-core, closed $p$-elastic curve.

中文翻译：

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$ S $ 2（G）$中以$ p $表示的闭合曲线和扁平芯闭合$ p $曲线的总曲率

我们考虑二维球中$ p $弹性曲线的变分问题。我们给出了它的第一个变化公式，在二维球体中，我们给出了一个满足第一个变化公式为零的解决方案的实现。我们还显示了扁芯闭合的$ p $弹性曲线的存在。