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

Invariant surfaces in homogenous space Sol with constant curvature