  A mixed type surface is a connected regular surface in a Lorentzian
3-manifold with non-empty spacelike and timelike point sets. The induced metric
of a mixed type surface is a signature-changing metric, and their lightlike
points may be regarded as singular points of such metrics. In this paper, we
investigate the behavior of Gaussian curvature at a non-degenerate lightlike
point of a mixed type surface. To characterize the boundedness of Gaussian
curvature at a non-degenerate lightlike points, we introduce several
fundamental invariants along non-degenerate lightlike points, such as the
lightlike singular curvature and the lightlike normal curvature. Moreover,
using the results by Pelletier and Steller, we obtain the Gauss-Bonnet type
formula for mixed type surfaces with bounded Gaussian curvature.
