Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Levi-Civita connections for conformally deformed metrics on tame
  differential calculi   Given a tame differential calculus over a noncommutative algebra
$\mathcal{A}$ and an $\mathcal{A}$-bilinear pseudo-Riemannian metric $g_0,$
consider the conformal deformation $ g = k. g_0, $ $k$ being an invertible
element of $\mathcal{A}.$We prove that there exists a unique connection
$\nabla$ on the bimodule of one-forms of the differential calculus which is
torsionless and compatible with $g.$ We derive a concrete formula connecting
$\nabla$ and the Levi-Civita connection for the pseudo-Riemannian metric $g_0.$
As an application, we compute the Ricci and scalar curvature for a general
conformal perturbation of the canonical metric on the noncommutative $2$-torus
as well as for a natural metric on the quantum Heisenberg manifold. For the
latter, the scalar curvature turns out to be a negative constant.

30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph