Derdzinski and Shen's theorem on the restrictions on the Riemann tensor imposed by the 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 compatible tensors, in particular those generated by geodesic mappings. Compatibility is extended to generalized curvature tensors, with an application to Weyl's tensor and general relativity.

Riemann compatible tensors / C.A. Mantica, L.G. Molinari. - In: COLLOQUIUM MATHEMATICUM. - ISSN 0010-1354. - 128:2(2012 Nov), pp. 197-210. [10.4064/cm128-2-5]

Riemann compatible tensors

C.A. Mantica;L.G. Molinari
Ultimo
2012

Abstract

Derdzinski and Shen's theorem on the restrictions on the Riemann tensor imposed by the 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 compatible tensors, in particular those generated by geodesic mappings. Compatibility is extended to generalized curvature tensors, with an application to Weyl's tensor and general relativity.
Codazzi tensor ; Riemann tensor ; Riemann compatibility ; generalized curvature tensor ; geodesic mapping ; Pontryagin forms
Settore MAT/03 - Geometria
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
nov-2012
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/215433
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