Total curvatures of a closed curve in Euclidean $n$-space
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- by L. Hernández Encinas and J. Muñoz Masqué PDF
- Proc. Amer. Math. Soc. 132 (2004), 2127-2132 Request permission
Abstract:
A classical result by J. W. Milnor states that the total curvature of a closed curve $C$ in the Euclidean $n$-space is the limit of the total curvatures of polygons inscribed in $C$. In the present paper a similar geometric interpretation is given for all total curvatures $\int _{C}|\kappa _{r}|\mathrm {d}s$, $r=1,\ldots ,n-1$.References
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Additional Information
- L. Hernández Encinas
- Affiliation: Instituto de Física Aplicada, Consejo Superior de Investigaciones Cientificas, Calle Serrano 144, 28006-Madrid, Spain
- Email: luis@iec.csic.es
- J. Muñoz Masqué
- Affiliation: Instituto de Física Aplicada, Consejo Superior de Investigaciones Cientificas, Calle Serrano 144, 28006-Madrid, Spain
- Email: jaime@iec.csic.es
- Received by editor(s): February 26, 2003
- Received by editor(s) in revised form: March 25, 2003
- Published electronically: January 23, 2004
- Additional Notes: This work was supported by Ministerio de Ciencia y Tecnología (Spain) under grants TIC2001–0586 and BFM2002–00141.
- Communicated by: Jon G. Wolfson
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2127-2132
- MSC (2000): Primary 53A04; Secondary 28A75, 51M20
- DOI: https://doi.org/10.1090/S0002-9939-04-07310-1
- MathSciNet review: 2053986