GROWTH OF LEAVES IN FOLIATIONS WITH EHRESMANN CONNECTIONS

Abstract

In this paper, we obtain a sufficient condition for a foliation $ℱ$ with an Ehresmann connection $\mathcal{D}={(\text{T}ℱ)}^{\perp }$ on a compact, connected manifold $M$ to have leaves whose universal covers have the same growth type. When such a foliation has a compact leaf $L$, we show that the growth type of all leaves is bounded from above by the growth types of ${\pi }_{1}L$ and $H_{\mathcal{D}}(L)$.