The curvature and torsion of curves in a surface

Let f be a function with certain properties and γ be a closed curve with the torsion τ . We prove that ∮ γ f τ d s = 0 if γ is a spherical curve, and conversely, if a surface makes the integral equal to zero for all closed curves, it is part of a sphere or a plane. This generalizes a known theorem o...

Ausführliche Beschreibung

Bibliographische Detailangaben

Veröffentlicht in:	Journal of geometry 2017-12, Vol.108 (3), p.1085-1090
Hauptverfasser:	Yin, Songting, Zheng, Daxiao
Format:	Artikel
Sprache:	eng
Schlagworte:	Curvature Geometry Mathematics Mathematics and Statistics Torsion
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!