Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics

Authors : Mosayeb ZOHREHVAND

Pages : 50-60

Doi:10.36890/iejg.566914

View : 14 | Download : 8

Publication Date : 2020-01-30

Article Type : Research Paper

Abstract :Let ‎$‎ insert ignore into journalissuearticles values(M,g); $ be a Riemannian manifold and ‎$‎ TM $ be its tangent bundle. ‎In the present paper‎, ‎we study infinitesimal projective transformations on $ TM $ with respect to the Levi-Civita connection of a class of insert ignore into journalissuearticles values(pseudo-);Riemannian metrics ‎$ ‎‎\tilde{g}‎ $ which is a generalization of the three classical lifts of the metric ‎$‎g$. We characterized this type of transformations and then ‎we prove that if $ insert ignore into journalissuearticles values(TM,‎\tilde{g}‎); $ admits a non-affine infinitesimal projective transformation‎, ‎then $ M $ and $ TM‎‎ $ are locally flat.
Keywords : Lift metrics, infinitesimal projective transformations, Riemannian manifold, tangent bundle, locally flat