J-Trajectories in 4-Dimensional Solvable Lie Group \(\mathrm {Sol}_0^4\)

Abstract

J-trajectories are arc length parameterized curves in almost Hermitian manifold which satisfy the equation \(\nabla _{{\dot{\gamma }}}{\dot{\gamma }}=q J {\dot{\gamma }}\). In this paper J-trajectories in the solvable Lie group \(\mathrm {Sol}_0^4\) are investigated. The first and the second curvature of a non-geodesic J-trajectory in an arbitrary LCK manifold whose anti Lee field has constant length are examined. In particular, the curvatures of non-geodesic J-trajectories in \(\mathrm {Sol}_0^4\) are characterized.