Geodesic
Invariants and flow geometry
Colloquium Mathematicum, Tome 81 (1999) no. 1, pp. 33-50.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We continue the study of Riemannian manifolds (M,g) equipped with an isometric flow $ℱ_ξ$ generated by a unit Killing vector field ξ. We derive some new results for normal and contact flows and use invariants with respect to the group of ξ-preserving isometries to charaterize special (M,g,$ℱ_ξ$), in particular Einstein, η-Einstein, η-parallel and locally Killing-transversally symmetric spaces. Furthermore, we introduce curvature homogeneous flows and flow model spaces and derive an algebraic characterization of Killing-transversally symmetric spaces by using the curvature tensor of special flow model spaces. All these results extend the corresponding theory in Sasakian geometry to flow geometry.
DOI : 10.4064/cm-81-1-33-50
Keywords: flow model spaces, normal, contact and curvature homogeneous flows, invariants and characterizations of special Riemannian manifolds, flows generated by a unit Killing vector field

J. González-Dávila 1 ; L. Vanhecke 1

1 
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J. González-Dávila; L. Vanhecke. Invariants and flow geometry. Colloquium Mathematicum, Tome 81 (1999) no. 1, pp. 33-50. doi : 10.4064/cm-81-1-33-50. http://geodesic.mathdoc.fr/articles/10.4064/cm-81-1-33-50/

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