an:04062169
Zbl 0651.57018
Saralegui, M.
The Euler class for flows of isometries
EN
Differential geometry, Proc. 5th Int. Colloq., Santiago de Compostela/Spain 1984, Res. Notes Math. 131, 220-227 (1985).
1985
a
57R30 57R20 53C12 57R15
flow of isometries; 1-dimensional orientable Riemannian foliation; Euler class; foliated bundle; contact flow
[For the entire collection see Zbl 0637.00004.]
A flow of isometries is defined as a 1-dimensional orientable Riemannian foliation \({\mathcal F}\) on a compact manifold M for which there exists a Riemannian metric g on M and a unit vector field Z tangent to \({\mathcal F}\) generating a group of isometries \((\psi_ t)\), \(t\in {\mathbb{R}}\). The Euler class of \({\mathcal F}\) is shown to vanish when (M,\({\mathcal F})\) is a foliated bundle and to be non-zero when \({\mathcal F}\) is a contact flow (i.e. when there exists a contact form \(\omega\) on M such that the unique vector field Y on M defind by \(\omega (Y)=1\) and \(d\omega (Y,\cdot)=0\) is tangent to \({\mathcal F})\).
P.Walczak
Zbl 0637.00004