Abstract
Xanthopoulos and Zannias have solved the coupled Einstein conformally invariant massless scalar field equations under the assumption that the metric admits a four-parameter group of isometries with spacelike generators when the three-parameter subgroup of isometries acts on two-dimensional surfaces of positive, negative, and zero curvature. In this paper all known independent second order curvature invariants of these metrics are constructed in order to discuss the scalar curvature singularities. The plane metrics are, except for a subset of measure zero, singular free.
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