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Invariants and flow geometry

J. González-Dávila;  L. Vanhecke — 1999

Colloquium Mathematicae

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...

Invariant harmonic unit vector fields on Lie groups

J. C. González-Dávila;  L. Vanhecke — 2002

Bollettino dell'Unione Matematica Italiana

We provide a new characterization of invariant harmonic unit vector fields on Lie groups endowed with a left-invariant metric. We use it to derive existence results and to construct new examples on Lie groups equipped with a bi-invariant metric, on three-dimensional Lie groups, on generalized Heisenberg groups, on Damek-Ricci spaces and on particular semi-direct products. In several cases a complete list of such vector fields is given. Furthermore, for a lot of the examples we determine associated...

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