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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
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