Remarks on Chebyshev coordinates.
Ricci and Bianchi identities for -normal -linear connections on .
Riemann compatible tensors
Derdziński and Shen's theorem on the restrictions on the Riemann tensor imposed by existence of a Codazzi tensor holds more generally when a Riemann compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann compatibility is equivalent to the Bianchi identity for a new "Codazzi deviation tensor", with a geometric significance. The above general properties are studied, with their implications on Pontryagin forms. Examples are given of manifolds with Riemann...
Riemannian manifolds with almost constant scalar curvature.