English

Minimizability of developable Riemannian foliations

Differential Geometry 2010-09-07 v3

Abstract

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.

Keywords

Cite

@article{arxiv.0909.4508,
  title  = {Minimizability of developable Riemannian foliations},
  author = {Hiraku Nozawa},
  journal= {arXiv preprint arXiv:0909.4508},
  year   = {2010}
}

Comments

15 pages, correction of misprints

R2 v1 2026-06-21T13:50:10.951Z