Homology, Homotopy and Applications
Volume 24 (2022)
Nondegenerate homotopy and geometric flows
Pages: 255 – 264
Formulating geometric flows of space curves using quantities derived from the Frenet frame restricts the motion to one connected component of the space of locally convex curves. A new invariant quantity called tangent turning sign is proposed to determine the nondegenerate homotopy type of the initial curve and identify its possible shapes during the geometric flow.
locally convex curve, geometric flow, nondegenerate homotopy
2010 Mathematics Subject Classification
14H50, 53C44, 55P15
This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic under the OP RDE grant number CZ.02.1.01/0.0/0.0/16 019/0000753 “Research centre for lowcarbon energy technologies”.
Received 5 October 2021
Received revised 12 November 2021
Accepted 17 November 2021
Published 24 August 2022