Saralegui, M. The Euler class for flows of isometries. (English) Zbl 0651.57018 Differential geometry, Proc. 5th Int. Colloq., Santiago de Compostela/Spain 1984, Res. Notes Math. 131, 220-227 (1985). [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 \({\mathcal F})\). Reviewer: P.Walczak Cited in 3 ReviewsCited in 6 Documents MSC: 57R30 Foliations in differential topology; geometric theory 57R20 Characteristic classes and numbers in differential topology 53C12 Foliations (differential geometric aspects) 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) Keywords:flow of isometries; 1-dimensional orientable Riemannian foliation; Euler class; foliated bundle; contact flow Citations:Zbl 0637.00004 PDFBibTeX XML