Geodesics and isocline distributions in tangent bundles of nonflat Lorentzian-Heisenberg spaces

Let (H3, g1) and (H3, g2) be the Lorentzian-Heisenberg spaces with nonflat metrics g1 and g2, and (TH3, gs 1), (TH3, gs 2) be their tangent bundles with the Sasaki metric, respectively. In the present paper, we find nontotally geodesic distributions in tangent bundles by using lifts of contact forms from the base manifold H3.We give examples for totally geodesic but not isocline distributions. We study the geodesics of tangent bundles by considering horizontal and natural lifts of geodesics of the base manifold H3. We also investigate more general classes of geodesics which are not obtained from horizontal and natural lifts of geodesics. © TÜBİTAK