AI 中文总结
研究将光滑实\(n\)维流形范畴嵌入结合簇范畴，把流形上联络解释推广到结合簇，最终证明结合簇中测地线存在，核心方法是范畴嵌入及联络推广，主要贡献是测地线存在性证明。
AI 中文摘要
我们已将光滑实\(n\)维流形的范畴忠实地嵌入到结合簇的范畴中。许多在光滑流形上的构造随后可推广到结合簇上。在此我们将把流形上联络的著名解释推广到结合簇上的联络，最终证明结合簇中测地线的存在性。
英文摘要
We have embedded the category of smooth real $n$-manifolds faithfully into the category of associative varieties, \cite{S2603}. Many constructions on smooth manifolds can then be generalized to associative varieties. Here we will generalize the well known interpretation of connections on manifolds to connections on associative varieties. This eventually proves the existence of geodesics in an associative variety.
