Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry

Constantin Călin; Mircea Crasmareanu

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 4, page 945-960
  • ISSN: 0011-4642

Abstract

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We study Legendre and slant curves for Bianchi-Cartan-Vranceanu metrics. These curves are characterized through the scalar product between the normal at the curve and the vertical vector field and in the helix case they have a proper (non-harmonic) mean curvature vector field. The general expression of the curvature and torsion of these curves and the associated Lancret invariant (for the slant case) are computed as well as the corresponding variant for some particular cases. The slant (particularly Legendre) curves which are helices are completely determined.

How to cite

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Călin, Constantin, and Crasmareanu, Mircea. "Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry." Czechoslovak Mathematical Journal 64.4 (2014): 945-960. <http://eudml.org/doc/269855>.

@article{Călin2014,
abstract = {We study Legendre and slant curves for Bianchi-Cartan-Vranceanu metrics. These curves are characterized through the scalar product between the normal at the curve and the vertical vector field and in the helix case they have a proper (non-harmonic) mean curvature vector field. The general expression of the curvature and torsion of these curves and the associated Lancret invariant (for the slant case) are computed as well as the corresponding variant for some particular cases. The slant (particularly Legendre) curves which are helices are completely determined.},
author = {Călin, Constantin, Crasmareanu, Mircea},
journal = {Czechoslovak Mathematical Journal},
keywords = {Bianchi-Cartan-Vranceanu metric; slant curve; Legendre curve; Lancret invariant; helix; Bianchi-Cartan-Vranceanu metric; slant curve; Legendre curve; Lancret invariant; helix},
language = {eng},
number = {4},
pages = {945-960},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry},
url = {http://eudml.org/doc/269855},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Călin, Constantin
AU - Crasmareanu, Mircea
TI - Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 945
EP - 960
AB - We study Legendre and slant curves for Bianchi-Cartan-Vranceanu metrics. These curves are characterized through the scalar product between the normal at the curve and the vertical vector field and in the helix case they have a proper (non-harmonic) mean curvature vector field. The general expression of the curvature and torsion of these curves and the associated Lancret invariant (for the slant case) are computed as well as the corresponding variant for some particular cases. The slant (particularly Legendre) curves which are helices are completely determined.
LA - eng
KW - Bianchi-Cartan-Vranceanu metric; slant curve; Legendre curve; Lancret invariant; helix; Bianchi-Cartan-Vranceanu metric; slant curve; Legendre curve; Lancret invariant; helix
UR - http://eudml.org/doc/269855
ER -

References

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