SL h (2)-Symmetric Torsionless Connections

Abstract

The most general 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, linearconnection, 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.