$K$ models and type IIB superstring backgrounds

A family of type IIB superstring backgrounds involving Ramond-Ramond fields are obtained in ten dimensions starting from a $K$ model through a generalization of our recent results. The unbroken global $\mathrm{SL}(2, R)$ symmetry of the type IIB equations of motion are implemented in this context as a solution generating transformation. A geometrical analysis, based on the tensor structure of the higher order ${\alpha }^{\prime }$ terms in the equations of motion, is employed to show that these backgrounds are exact.