  The authors define a SNS (semi-nearly-sub)-Riemannian connection on nearly
sub-Riemannian manifolds and study the geometric properties of such a
connection, and obtain the natures of horizontal curvature tensors between
horizontal sub-Riemannian connection and SNS-Riemannian connection. The authors
further investigate the geometric characteristics of the projective
SNS-Riemannian connection, and obtain a necessary and sufficient condition for
a nearly sub-Riemannian manifold being projectively flat.
