RIEMANNIAN METRIC DETERMINED FROM THE CONTACT STRUCTURE ON PROJECTIVISED TANGENT BUNDLES

Sasaki type metric was considered by Endo and Fueki as a Riemannian metric constructing a contact metric structure deduced from the contact structure on the projectivised tangent bundle PTM [Nonlinear Anal., Real World Appl., 10(2009), 191- 202]. In this paper, we study a more generalized Riemannian metric (h-v metric) [R. Miron and M. Anastasiei: Vector Bundles. Lagrange Spaces. Applications in Relativity Theory, Ed. Acad., Bucharest, 1987 (in Romanian)] determined from the contact structure on PTM.