Riemann compatible tensors

Carlo Alberto Mantica, and Luca Guido Molinari. "Riemann compatible tensors." Colloquium Mathematicae 128.2 (2012): 197-210. <http://eudml.org/doc/283873>.

@article{CarloAlbertoMantica2012,
abstract = {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 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.},
author = {Carlo Alberto Mantica, Luca Guido Molinari},
journal = {Colloquium Mathematicae},
keywords = {Codazzi tensor; Riemann tensor; Riemann compatibility; generalized curvature tensor; geodesic mapping; Pontryagin forms},
language = {eng},
number = {2},
pages = {197-210},
title = {Riemann compatible tensors},
url = {http://eudml.org/doc/283873},
volume = {128},
year = {2012},
}

TY - JOUR
AU - Carlo Alberto Mantica
AU - Luca Guido Molinari
TI - Riemann compatible tensors
JO - Colloquium Mathematicae
PY - 2012
VL - 128
IS - 2
SP - 197
EP - 210
AB - 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 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.
LA - eng
KW - Codazzi tensor; Riemann tensor; Riemann compatibility; generalized curvature tensor; geodesic mapping; Pontryagin forms
UR - http://eudml.org/doc/283873
ER -