## A pseudo projective curvature tensor on a Riemannian manifold.(English)Zbl 1028.53016

The pseudo projective curvature tensor $$\overline P$$ of a Riemannian manifold $$(M,g)$$ is obtained by modifying the Riemann curvature tensor of $$(M,g)$$ in a specific way, using the metric, the Ricci curvature and the scalar curvature. In this note, the author studies manifolds which are pseudo projectively flat ($$\overline P=0$$) or pseudo projectively conservative $$(\operatorname {div}\overline P=0)$$.

### MSC:

 53B20 Local Riemannian geometry