  Let $M^2$ be an oriented 2-manifold and $f:M^2\to R^3$ a $C^\infty$-map. A
point $p\in M^2$ is called a singular point if $f$ is not an immersion at $p$.
The map $f$ is called a front (or wave front), if there exists a unit
$C^\infty$-vector field $\nu$ such that the image of each tangent vector
$df(X)$ $(X\in TM^2)$ is perpendicular to $\nu$, and the pair $(f,\nu)$ gives
an immersion into $R^3\times S^2$. In our previous paper, we gave an intrinsic
formulation of wave fronts in $R^3$. In this paper, we shall investigate the
behavior of cuspidal edges near corank one singular points and establish
Gauss-Bonnet-type formulas under the intrinsic formulation.
