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The most general $\text{SL}_h(2)$-symmetric torsionless linear connection is
constructed. This is done based on a recently proposed definition of a linear
connection in noncommutative geometry. Part of the results can be obtained by
using the singular map which relates the $q$-plane to the $h$-plane. There is
also a part in the covariant derivative, linear connection, and curvature which
does not have any $q$-analogue. It is seen that the covariant derivative of the
$h$-plane is `more classical' or `less quantized' than that of the $q$-plane.
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