Geodesic rigidity of Levi-Civita connections admitting essential projective vector fields
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In this paper, it is proved that a connected 3-dimensional Riemannian manifold or a closed connected semi-Riemannian manifold \(M^n\) (\(n>1\)) admitting a projective vector field with a non-linearizable singularity is projectively flat.
KeywordsGeodesic rigidity Essential projective vector field Metrizable projective structure Local dynamics
Mathematics Subject Classification (2000)53A20
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