EUDML

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...

Geodesic spheres and isometric flows

J. González-Dávila; L. Vanhecke — 1994

Colloquium Mathematicae

Steiner's formula for the volume of a parallel hypersurface in a riemannian manifold

E. Abbena; A. Gray; L. Vanhecke — 1981

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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...

The Chern numbers of holomorphic vector bundles and formally holomorphic connections of complex vector bundles over almost complex manifolds.

L. Vanhecke; A. Gray; M. Barros; A.M. Naveira — 1980

Journal für die reine und angewandte Mathematik

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Mean and scalar curvature homogeneous Riemannian manifolds.

...-Kongruenzen von Vincensini und Verallgemeinerungen der Kongruenzen mit einer Minimalfläche als Mittelhüllfläche.

Interaction of Tubes and Spheres.

Naturally reductive homogeneous spaces and generalized Heisenberg groups

A New Formula for the Shape Operator of a Geodesic Sphere and Its Applications.

Sur les variétés lorentziennes munies d'une connexion principale

Curvature homogeneous riemannian manifolds

New Examples of Weakly Symmetric Spaces.

Differential geometry of geodesic spheres.

Invariants and flow geometry

Geodesic spheres and isometric flows

Steiner's formula for the volume of a parallel hypersurface in a riemannian manifold

Invariant harmonic unit vector fields on Lie groups

The Chern numbers of holomorphic vector bundles and formally holomorphic connections of complex vector bundles over almost complex manifolds.