A novel approach to the connection theory on a differential manifold is presented here. In this framework, the notion of a $k$-th order ($k=1,2,\dots$) curvature tensor arises in a natural way. For $k=1$ our curvature tensor is equivalent to the conventional Riemann tensor. This approach provides natural tools for analysis of higher order variational problems in General Relativity Theory.

中文翻译：

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连接的协变射流和高阶曲率张量

本文介绍了一种关于差动歧管连接理论的新颖方法。在这个框架中，$ķ$-第顺序$ķ=\mathrm{1个}，2，\dots$）曲率张量以自然的方式出现。对于$ķ=\mathrm{1个}$我们的曲率张量等于常规的黎曼张量。这种方法为分析广义相对论中的高阶变分问题提供了自然的工具。