Abstract
In this chapter we take a completely different approach to the study of volumes of tubes. We shall compute the first few terms of the power series of the volume function \(V_P^M(r)\) as a function of r. In the same issue of the American Journal of Mathematics in which Weyl’s paper [Weyl1] appeared in 1939, there is an article [Ht] by the statistician Hotelling. In it Hotelling computes the first two nonzero terms of the expansion for \(V_P^M(r)\) in the case that P is a curve in an arbitrary Riemannian manifold M. In fact, Weyl’s paper is partially a response to Hotelling’s paper. Hotelling discusses several applications of tube formulas to statistics.
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© 2004 Springer Basel AG
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Gray, A. (2004). Power Series Expansions for Tube Volumes. In: Tubes. Progress in Mathematics, vol 221. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7966-8_9
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DOI: https://doi.org/10.1007/978-3-0348-7966-8_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9639-9
Online ISBN: 978-3-0348-7966-8
eBook Packages: Springer Book Archive