Changes in the transverse curvature of the sigma model in the presence of a constant non-commutator

We study the transverse curvature of the sigma model in the presence of a constant non-commutator and analyze the effect of the constant non-commutator on the transverse curvature in the sigma model. We analyze the transverse curvature in the sigma model in two different contexts: one is the classical sigma model in the presence of a constant non-commutator, and the other is the quantum sigma model in the presence of a constant non-commutator.