T-symmetry in String Geometry Theory

String geometry theory is one of the candidates of non-perturbative formulation of string theory. In this paper, we have shown that dimensionally reduced string geometry theories have what we call T-symmetry. In case of the dimensional reduction in space-like directions, the T-symmetry transformation gives the T-dual transformation between the type IIA and IIB perturbative vacua. In case of the dimensional reduction in the direction of string geometry time $\bar{\tau}$, the T-symmetry transformation is independent of the T-dual transformation, and gives a symmetry that cannot be seen in the perturbative string theories.