Abstract
For a curve in an n-dimensional Euclidean space En which obeys certain conditions of regularity, to each point of the curve there is put in correspondence (n − 1) numbers of k1, k2, ... , kn − 1 of the curvatures at the point of the curve. Let us set
where integration is carried out with respect to the arc length. The functions obtained in this way will be called integral curvatures of the curve. There arises a problem — to give such a definition of the ith integral curvature which could be applied to an essentially wider class of curves than the class considered in differential geometry. Accordingly, the contents of Chapter V can be considered as a theory of the curves of a limited integral first curvature. Chapter IV presents a theory of curves of a limited integral first curvature in a space Sn.
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© 1989 Kluwer Academic Publishers
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Alexandrov, A.D., Reshetnyak, Y.G. (1989). Some Additional Remarks. In: General Theory of Irregular Curves. Mathematics and Its Applications, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2591-5_11
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DOI: https://doi.org/10.1007/978-94-009-2591-5_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7671-5
Online ISBN: 978-94-009-2591-5
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