%0 Journal Article %T On the Gauss curvature of compact surfaces in homogeneous 3-manifolds %A Francisco Torralbo %A Francisco Urbano %J Mathematics %D 2009 %I arXiv %X Compact flat surfaces of homogeneous Riemannian 3-manifolds with isometry group of dimension 4 are classified. Non-existence results for compact constant Gauss curvature surfaces in these 3-manifolds are established. %U http://arxiv.org/abs/0903.1735v1