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Foliations with leaves of nonpositive curvature

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Abstract

We answer a question of Gromov ([G2]) in the codimension 1 case: ifF is a codimension 1 foliation of a compact manifoldM with leaves of negative curvature, thenπ 1(M) has exponential growth. We also prove a result analogous to Zimmer’s ([Z2]): ifF is a codimension 1 foliation on a compact manifold with leaves of nonpositive curvature, and ifπ 1(M) has subexponential growth, then almost every leaf is flat. We give a foliated version of the Hopf theorem on surfaces without conjugate points.

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Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, 218 McAllister Building, 16802, University Park, PA, USA

    Chengbo Yue

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  1. Chengbo Yue
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Correspondence to Chengbo Yue.

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Partially supported by NSF Grant #DMS 9403870.

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Yue, C. Foliations with leaves of nonpositive curvature. Isr. J. Math. 97, 113–123 (1997). https://doi.org/10.1007/BF02774030

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  • DOI: https://doi.org/10.1007/BF02774030

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