Curvature computations for n-manifolds in Rn+m and solution to an open problem proposed by R. Goldman

In this paper, simple and explicit formulas for computing mean curvature vector and Gauss–Kronecker curvature for n-manifolds in Rn+m are derived. Using these formulas, we solve an open problem, proposed by Ron Goldman, about curvature formulas for implicit surfaces with higher co-dimensions.