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The b-boundary is a mathematical tool able to attach a topo- logical boundary to incomplete Lorentzian manifolds using a Riemani- ann metric called the Schmidt metric on the frame bundle. This has been a motivation for using the b-boundary to study gravitational sin- gularities in General Relativity. In this paper we give the general form of the Schmidt metric in the case of 1 + 1 Lorentzian manifolds. Fur- thermore, we give a general formula for the Ricci scalar of the Schmidt metric in terms of the Ricci scalar of the Lorentzian manifold and calcu- late explicitly the curvature of the Schmidt metric for several Lorentzian surfaces.

Lorentzian surfaces and the curvature of the Schmidt metric