Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2023; 38(4): 1261-1269

Online first article October 13, 2023      Printed October 31, 2023

https://doi.org/10.4134/CKMS.c230024

Copyright © The Korean Mathematical Society.

The flow-curvature of curves in a geometric surface

Mircea Crasmareanu

University ``Al. I. Cuza"

Abstract

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For a fixed parametrization of a curve in an orientable two-dimensional Riemannian manifold, we introduce and investigate a new frame and curvature function. Due to the way of defining this new frame as being the time-dependent rotation in the tangent plane of the standard Frenet frame, both these new tools are called flow.

Keywords: Two-dimensional Riemannian manifold, geodesic curvature, flow-frame, flow-curvature

MSC numbers: Primary 53A04, 53A45, 53A55

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