Geodesic rigidity of Levi-Civita connections admitting essential projective vector fields

  • Tianyu MaEmail author
Original Paper


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.


Geodesic rigidity Essential projective vector field Metrizable projective structure Local dynamics 

Mathematics Subject Classification (2000)




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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsFriedrich Schiller University JenaJenaGermany

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