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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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Riemannian Submanifolds. In: Generalized Curvatures. Geometry and Computing, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73792-6_11
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DOI: https://doi.org/10.1007/978-3-540-73792-6_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73791-9
Online ISBN: 978-3-540-73792-6
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