Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Levi-Civita connections and vector fields for noncommutative
  differential calculi   We study covariant derivatives on a class of centered bimodules $\mathcal{E}$
over an algebra A. We begin by identifying a $\mathbb{Z} ( A ) $-submodule $
\mathcal{X} ( A ) $ which can be viewed as the analogue of vector fields in
this context; $ \mathcal{X} ( A ) $ is proven to be a Lie algebra. Connections
on $\mathcal{E}$ are in one to one correspondence with covariant derivatives on
$ \mathcal{X} ( A ). $ We recover the classical formulas of torsion and metric
compatibility of a connection in the covariant derivative form. As a result, a
Koszul formula for the Levi-Civita connection is also derived.

29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci