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Displaying similar documents to “On Subspaces of Riemann-Otsuki Space”

Riemann compatible tensors

Carlo Alberto Mantica, Luca Guido Molinari (2012)

Colloquium Mathematicae

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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...