<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

Online veröffentlicht: 27. März 2023

Seitenbereich: 61 - 70

Eingereicht: 22. Juli 2022

Akzeptiert: 29. Dez. 2022

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

Schlüsselwörter
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

Online veröffentlicht: 27. März 2023

Seitenbereich: 61 - 70

Eingereicht: 22. Juli 2022

Akzeptiert: 29. Dez. 2022

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

Schlüsselwörterplane 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.

Schlüsselwörter
plane curve, angular vector field, rotational curvature