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arXiv · 2406.05503

Topology and bottom spectrum of transversally negatively curved foliations

Fabrice Baudoin
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Abstract

We show that for any Riemannian foliation with a simply connected and negatively curved leaf space the normal exponential map of a leaf is a diffeomorphism. As an application, if the leaves are furthermore minimal submanifolds, we give a sharp estimate for the bottom of the spectrum of such a Riemannian manifold. Our proof of the spectral estimate also yields an estimate for the bottom of the spectrum of the horizontal Laplacian.

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Fabrice Baudoin. 2024-06-08. Topology and bottom spectrum of transversally negatively curved foliations. https://arxiv.org/abs/2406.05503

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