Abstract:Our study is mainly devoted to a natural diagonal metric G on the total space
TMof the tangent bundle of a Riemannian manifold (M, 1). We provide the
necessary and sufficient conditions under which (TM,G) is a space form, or
equivalently (TM,G) is projectively Euclidean. Moreover, we classify the
natural diagonal metrics G for which (TM,G) is horizontally projectively flat
(resp. vertically projectively flat).
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