Metrics, connections and curves on tangent manifold

METRICS, CONNECTIONS AND CURVES ON TANGENT MANIFOLD (M. fla, Thesis) r Aysel TURGUT GAZ t UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOLOGY February 1989 ABSTRACT The main metrioa and connections on the tangent manifold of a differentiflble manifold, which can be !> obtained from a Riemanniftn metric and a linear connection on the manifold, were classified. In addition, higher order curvatures of the horizontal lift, natural lift and projectable curves on the tangent manifold corres ponding to any given curve on the manifold were calcula ted and so the relationships with the original curve were studied. -il-