Slant curves and particles in three-dimensional warped products and their Lancret invariants

Authors

  • C. Calin Technical University "Gh. Asachi" Iasi, Romania
  • M. Crasmareanu

Keywords:

warped product, slant curve, Legendre curve, Lancret invariant, Frenet frame.

Abstract

Slant curves are introduced in three-dimensional warped products with Euclidean factors; these curves are characterized through the scalar product between the normal at the curve and the vertical vector field and an important feature is that the case of constant Frenet curvatures implies a proper mean curvature vector field. A Lancret invariant is obtained and the Legendre curves are analyzed as particular case. An example of a slant curve is given for the exponential warping function; our example illustrates a proper (i.e. not reducible to the two dimensions) case of the Lancret Theorem of $3$-dimensional hyperbolic geometry. We point out an eventually relationship with the geometry of relativistic models. 10.1017/S0004972712000809

Published

2013-07-23

Issue

Vol. 88 No. 1 (2013)

Section

Articles
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