算术Levi-Civita连接
Arithmetic Levi-Civita connection
摘要：
本文是一系列文件的一部分，其中一个算术模拟经典微分几何正在开发。在这算术微分几何函数被替换为整数，导子被替换为费马商算子，和连接（分别曲率）被替换为某些adelic（分别全球）对象附加到对称矩阵与整数系数。以前的文件致力于一个算术模拟的陈连接。本文主要研究列维-奇维塔联络的一个算术模拟。
英文摘要：
This paper is part of a series of papers where an arithmetic analogue of classical differential geometry is being developed. In this arithmetic differential geometry functions are replaced by integer numbers, derivations are replaced by Fermat quotient operators, and connections (respectively curvature) are replaced by certain adelic (respectively global) objects attached to symmetric matrices with integral coefficients. Previous papers were devoted to an arithmetic analogue of the Chern connection. The present paper is devoted to an arithmetic analogue of the Levi-Civita connection.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
