Geodesic
On the number of nontrivial projective transformations of closed manifolds
Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 2, pp. 125-131.

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We show that for a closed Riemannian manifold the quotient of the group of projective transformations by the group of isometries contains at most two elements unless the metric has constant positive sectional curvature or every projective transformation is an affine transformation. 
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V. S. Matveev. On the number of nontrivial projective transformations of closed manifolds. Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 2, pp. 125-131. http://geodesic.mathdoc.fr/item/FPM_2015_20_2_a8/

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