The characterizations when two natural upper bounds of the set of copulas with a given diagonal section are copulas have been well studied in the literature. Given a curvilinear section, however, there is only a partial result concerning the characterization when a natural upper bound of the set of copulas is a copula. In this paper, we completely solve the characterization problem for this natural upper bound to be a copula in the curvilinear case.

翻译：具有特定对角截面的联结函数集的两个自然上界何时为联结函数的刻画问题已在文献中得到充分研究。然而，对于给定曲线截面，关于该集合的一个自然上界是否为联结函数的刻画仅存在部分结果。本文在曲线情形下完全解决了这一自然上界成为联结函数的刻画问题。