Positive scalar curvature on foliations: the noncompact case

Abstract

Let $(M,g^{TM})$ be a noncompact (not necessarily complete) enlargeable Riemannian manifold in the sense of Gromov-Lawson and $F$ an integrable subbundle of $TM$ . Let $k^F$ be the leafwise scalar curvature associated to $g^F=g^{TM}{|}_F$. We show that if either $TM$ or $F$ is spin, then $\inf (k^F)\le 0$. This generalizes the famous result of Gromov-Lawson on enlargeable manifolds to the case of foliations. It also extends an ansatz of Gromov on hyper-Euclidean spaces to general enlargeable Riemannian manifolds, as well as recent results on compact enlargeable foliated manifolds due to Benameur-Heitsch et al to the noncompact situation.

14 pages, revised version to appear in Advances in Mathematics

Cited by in corpus (1)

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