  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.
