The rotational curvature of plane curves

Mircea Crasmareanu

doi:10.2478/auom-2023-0019

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The rotational curvature of plane curves

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 31 (2023): Issue 2 (March 2023)

By: Mircea Crasmareanu

Open Access

|Mar 2023

Abstract

We introduce and study a new curvature function for plane curves inspired by the weighted mean curvature of M. Gromov. We call it rotational being the difference between the usual curvature and the inner product of the normal vector field and the angular vector field. But, since the problem of vanishing of this curvature involves complicated expressions we define a second rotational curvature. Both these curvatures are computed for several examples.

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2023-0019 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 61 - 70

Submitted on: Jul 22, 2022

Accepted on: Dec 29, 2022

Published on: Mar 27, 2023

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

plane curve,

angular vector field,

rotational curvature

Related subjects:

Mathematics,

General mathematics

© 2023 Mircea Crasmareanu, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 31 (2023): Issue 2 (March 2023)