Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry

Czechoslovak Mathematical Journal

Mircea Crasmareanu⁴  Constantin Clin⁶ 

[1] , Faculty of Mathematics, University "Al. 11, Iai, 700506, Romania;21, Iai, 700050, Romania,;Asachi", Bd. Cuza", Bd. Carol Department of Mathematics, Technical University "Gh. Dimitrie Mangeron, no. I, no. I. 

关键词: Bianchi-Cartan-Vranceanu metric;    slant curve;    Legendre curve;    Lancret invariant;    helix;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown