On projective transformations of complete Riemannian manifolds with constant scalar curvature
The author proves two theorems for a complete and simply connected Riemannian manifold \((M,g)\) of dimension \(n>2\) with a constant scalar curvature \(R\). If there exists a non-affine projective transformation of \((M,g)\) which leaves either the gravitational tensor field (where \(R>0\)) or the covariant derivative of Weyl's projective curvature tensor invariant, then \((M,g)\) is isometric to a Euclidean sphere.
scientific article; zbMATH DE number 1626287