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

Abstract

: Let ( H 3 , g 1 ) and ( H 3 , g 2 ) be the Lorentzian-Heisenberg spaces with nonflat metrics g 1 and g 2 , and ( TH 3 , g s 1 ) , ( TH 3 , g s 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 H 3 . 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 H 3 . We also investigate more general classes of geodesics which are not obtained from horizontal and natural lifts of geodesics.