  A surface in homogenous space Sol is said to be an invariant surface if it is
invariant under some of the two 1-parameter groups of isometries of the ambient
space whose fix point sets are totally geodesic surfaces. In this work we study
invariant surfaces that satisfy a certain condition on their curvatures. We
classify invariant surfaces with constant mean curvature and constant Gaussian
curvature. Also, we characterize invariant surfaces that satisfy a linear
Weingarten relation.
