Minimizability of developable Riemannian foliations

Details Minimizability of developable Riemannian foliations Minimizability of developable Riemannian foliations

2009-09-24

arxiv.org/abs/0909.4508v3

Ann. Global Anal. Geom. 38, Issue 2 119 - 133 (2010)

Mathematics

Differential Geometry

15 pages, correction of misprints

Scientific paper

10.1007/s10455-010-9203-7

Let (M,F) be a closed manifold with a Riemannian foliation. We show that the secondary characteristic classes of the Molino's commuting sheaf of (M,F) vanish if (M,F) is developable and the fundamental group of M is of polynomial growth. By theorems of \'{A}lvarez L\'{o}pez, our result implies that (M,F) is minimizable under the same conditions. As a corollary, we show that (M,F) is minimizable if F is of codimension 2 and the fundamental group of M is of polynomial growth.

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