Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics
Let $ (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 (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 $ (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,
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- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2008
- Yayıncı: Prof.Dr. H.Hilmi Hacısalioğlu