In Chap. 16, we have seen that the volume of the parallel body of a convex body with smooth boundary is a polynomial whose coefficients depend on the second fundamental form of the boundary. This formula has been generalized by Weyl [82] for the volume of tubes around any smooth submanifold in EN, with or without boundary.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Tubes Formula. In: Generalized Curvatures. Geometry and Computing, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73792-6_17
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DOI: https://doi.org/10.1007/978-3-540-73792-6_17
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