Invariants and flow geometry
Tom 81 / 1999
Colloquium Mathematicum 81 (1999), 33-50
DOI: 10.4064/cm-81-1-33-50
Streszczenie
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.
