Lagrange spaces with indicatrices as constant mean curvature surfaces or minimal surfaces.
Tzitzeica figuratrices in Hamilton geometry.
Nonlinear connections and semisprays on tangent manifolds.
Quadratic homogeneous ODE systems of Jordan-rigid body type.
Cylindrical Tzitzeica curves implies forced harmonic oscillators.
Exempls of conics arising in two-dimensional Finsler and Lagrange geometries.
From the Eisenhart problem to Ricci solitons in -Kenmotsu manifolds.
Trace decomposition and recurrency
Particular trace decompositions and applications of trace decomposition to almost projective invariants
First, by using the formulae of Krupka, the trace decomposition for some particular classes of tensors of types (1, 2) and (1, 3) is obtained. Second, it is proved that the traceless part of a tensor is an almost projective invariant of weight 1. We apply this result to Weyl curvature tensors.
Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry
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...
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