Extrinsic curvature and conformal Gauss–Bonnet for four-manifolds with corner

This paper defines two new extrinsic curvature quantities on the corner of a four-dimensional Riemannian manifold with corner. One these is pointwise conformal invariant, and transformation other governed by linear second-order conformally invariant partial differential operator. The Gauss-Bonnet theorem then stated in terms quantities.