Curvature Computations of 2-Manifolds in $\mathbb{R}^k$ (Journal of Computational Mathematics, 2021)
In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in $R^k$ with $k≥3$.
Keywords: Riemannian curvature; Mean curvature vector; Principal curvatures; Principal directions.