Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a type of semi-sub-Riemannian connection on a sub-Riemannian manifold   The authors first in this paper define a semi-symmetric metric non-holonomic
connection (called in briefly a semi-sub-Riemannian connection) on
sub-Riemannian manifolds, and study the relations between sub-Riemannian
connections and semi-sub-Riemannian connections. An invariant under a
connection transformation $\nabla\rightarrow D$ is obtained. The authors then
further deduce a sufficient and necessary condition that a sub-Riemannian
manifold associated with a semi-sub-Riemannian connection is flat, and derive
that a sub-Riemannian manifold with vanishing curvature with respect to
semi-sub-Riemannnian connection $D$ is a group manifold if and only if it is of
constant curvature.

1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th