Abstract
Smooth Riemannian submanifolds in Euclidean spaces are the smooth objects, on which we shall test the curvature measures defined in the next chapters. They are the direct generalization in any dimension and codimension of curves and surfaces in E3. Their extrinsic curvatures generalize the Gauss and mean curvatures of surfaces. We review (without proof) some fundamental notions on the subject. Classical books on Riemannian submanifolds are [26, 27].
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