Geodesic
Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 945-960.

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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.
DOI : 10.1007/s10587-014-0145-2
Classification : 53A55, 53B25, 53C25, 53D15
Keywords: Bianchi-Cartan-Vranceanu metric; slant curve; Legendre curve; Lancret invariant; helix 
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Călin, Constantin; Crasmareanu, Mircea. Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 945-960. doi : 10.1007/s10587-014-0145-2. http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0145-2/

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