Total curvature and some characterizations of closed curves in \(\mathrm{CAT}(k)\) spaces

DOI10.1007/s10711-018-0349-yzbMath1414.51007OpenAlexW2793900405WikidataQ130112640 ScholiaQ130112640MaRDI QIDQ1736086

Aniruth Phon-on, Areeyuth Sama-Ae

Publication date: 29 March 2019

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-018-0349-y

zbMATH Keywords

total curvatureclosed curve\(\mathrm{CAT}(k)\)

Mathematics Subject Classification ID

Distance geometry (51K99)

Cites Work

• Total curvature of curves in Riemannian manifolds
• Geometry of curves on spheres in CAT (\(\kappa\)) spaces
• On the total absolute curvature of closed curves in spheres
• The isoperimetric inequality and the total absolute curvature of closed curves in spheres
• The total absolute curvature of closed curves in Riemannian manifolds
• Total curvature and length estimate for curves in CAT(\(K\)) spaces.
• Comparison theorems for curves of bounded geodesic curvature in metric spaces of curvature bounded above
• On the total absolute curvature of closed curves in manifolds of negative curvature
• On the total curvature of knots
• Generalized Riemannian spaces
• The Fary-Milnor theorem in Hadamard manifolds
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