We continue the study of Riemannian manifolds (M,g) equipped with an isometric flow 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,), 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.
@article{bwmeta1.element.bwnjournal-article-cmv81i1p33bwm,
author = {J. Gonz\'alez-D\'avila and L. Vanhecke},
title = {Invariants and flow geometry},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {33-50},
zbl = {0936.53030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv81i1p33bwm}
}
González-Dávila, J.; Vanhecke, L. Invariants and flow geometry. Colloquium Mathematicae, Tome 79 (1999) pp. 33-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv81i1p33bwm/
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