Generalized Einstein manifolds

Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1990), p. [49]-58 / Harvested from

Résumé

[For the entire collection see Zbl 0699.00032.] A manifold (M,g) is said to be generalized Einstein manifold if the following condition is satisfied $(\nabla_{X} S) (Y, Z) = σ (X) g (Y, Z) + ν (Y) g (X, Z) + ν (Z) g (X, Y)$ where S(X,Y) is the Ricci tensor of (M,g) and $σ$ (X), $ν$ (X) are certain $ℓ$ -forms. In the present paper the author studies properties of conformal and geodesic mappings of generalized Einstein manifolds. He gives the local classification of generalized Einstein manifolds when g( $ψ$ (X), $ψ$ (X)) $\neq 0$ .

MR MR1061788 | Zbl 0704.53040

EUDML-ID : urn:eudml:doc:221308
Mots clés:

@article{701461,
     title = {Generalized Einstein manifolds},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1990},
     pages = {[49]-58},
     mrnumber = {MR1061788},
     zbl = {0704.53040},
     url = {http://dml.mathdoc.fr/item/701461}
}

Formella, Stanisław. Generalized Einstein manifolds, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1990), pp. [49]-58. http://gdmltest.u-ga.fr/item/701461/