<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We introduce and study a new curvature function for plane curves inspired by the weighted mean curvature of M. Gromov. We call it <italic>rotational</italic> 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.</p>
</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.

The rotational curvature of plane curves

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"The rotational curvature of plane curves"}

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...

The rotational curvature of plane curves

Pubblicato online: 27 mar 2023

Pagine: 61 - 70

Ricevuto: 22 lug 2022

Accettato: 29 dic 2022

DOI: https://doi.org/10.2478/auom-2023-0019

Parole chiave
plane curve, angular vector field, rotational curvature

© 2023 Mircea Crasmareanu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The rotational curvature of plane curves

Pubblicato online: 27 mar 2023

Pagine: 61 - 70

Ricevuto: 22 lug 2022

Accettato: 29 dic 2022

DOI: https://doi.org/10.2478/auom-2023-0019

Parole chiaveplane curve, angular vector field, rotational curvature

© 2023 Mircea Crasmareanu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Parole chiave
plane curve, angular vector field, rotational curvature