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 R^n^+^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.

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