Generalized Einstein manifolds

Formella, Stanisław

  • Proceedings of the Winter School "Geometry and Physics", Publisher: Circolo Matematico di Palermo(Palermo), page [49]-58

Abstract

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[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 ( ∇ 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)) ≠ 0 .

How to cite

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Formella, Stanisław. "Generalized Einstein manifolds." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1990. [49]-58. <http://eudml.org/doc/221308>.

@inProceedings{Formella1990,
abstract = {[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 \[ (\nabla \_XS)(Y,Z)=\sigma (X)g(Y,Z)+\nu (Y)g(X,Z)+\nu (Z)g(X,Y) \] where S(X,Y) is the Ricci tensor of (M,g) and $\sigma $ (X), $\nu $ (X) are certain $\ell $-forms. In the present paper the author studies properties of conformal and geodesic mappings of generalized Einstein manifolds. He gives the local classification of generalized Einstein manifolds when g($\psi $ (X),$\psi $ (X))$\ne 0$.},
author = {Formella, Stanisław},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Geometry; Physics; Proceedings; Winter school; Srní (Czechoslovakia)},
location = {Palermo},
pages = {[49]-58},
publisher = {Circolo Matematico di Palermo},
title = {Generalized Einstein manifolds},
url = {http://eudml.org/doc/221308},
year = {1990},
}

TY - CLSWK
AU - Formella, Stanisław
TI - Generalized Einstein manifolds
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1990
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [49]
EP - 58
AB - [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 \[ (\nabla _XS)(Y,Z)=\sigma (X)g(Y,Z)+\nu (Y)g(X,Z)+\nu (Z)g(X,Y) \] where S(X,Y) is the Ricci tensor of (M,g) and $\sigma $ (X), $\nu $ (X) are certain $\ell $-forms. In the present paper the author studies properties of conformal and geodesic mappings of generalized Einstein manifolds. He gives the local classification of generalized Einstein manifolds when g($\psi $ (X),$\psi $ (X))$\ne 0$.
KW - Geometry; Physics; Proceedings; Winter school; Srní (Czechoslovakia)
UR - http://eudml.org/doc/221308
ER -

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