An extension of the fenchel theorem |
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| Authors: | Antonella Carfagna D'Andrea Giuliano Romani |
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| Affiliation: | (1) Dip. Metodi e Modelli Matematici per le Scienze Applicate, Via A. Scarpa, 10, I-00161 Roma, Italy;(2) Dip. Matematica !["lsquo"]("/content/w126875478674n02/xlarge8216.gif") G. Castelnuovo!["rsquo"]("/content/w126875478674n02/xlarge8217.gif") , P. le Aldo Moro, 5, I-00185 Roma, Italy |
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| Abstract: | We give an extension of the Fenchel-Borsuk result by introducing the total absolute torsion-curvature KT( ) for regular curves whose tangent indicatrix is a piecewise regular curve ( -closed curves). We prove that KT() is low bounded by 2 and we give a geometric characterization for the -closed curves whose KT() is minimal. |
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