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The rotational curvature of plane curves

The rotational curvature of plane curves AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analele Universitatii Ovidius Constanta - Seria Matematica de Gruyter

The rotational curvature of plane curves

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Publisher
de Gruyter
Copyright
© 2023 Mircea Crasmareanu, published by Sciendo
eISSN
1844-0835
DOI
10.2478/auom-2023-0019
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Analele Universitatii Ovidius Constanta - Seria Matematicade Gruyter

Published: Mar 1, 2023

Keywords: plane curve; angular vector field; rotational curvature; Primary 53A04; Secondary 53A45, 53A55

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