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arXiv · 2604.01415

Totally Geodesic Submanifolds in Products of Non-Positively Curved Manifolds

Nicholas Hanson
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Abstract

We study non-positively curved closed manifolds $M$ and $n$-dimensional totally geodesic submanifolds of $M \times M$ which satisfy a transversality condition. We prove that, under some mild irreducibility requirements on $M$, if $M \times M$ admits infinitely many such submanifolds or just a single dense such submanifold, then $M$ is a locally symmetric space. In proving this, we prove a stronger version which only requires such submanifolds to exist in the universal cover $\widetilde M \times \widetilde M$.

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Nicholas Hanson. 2026-04-01. Totally Geodesic Submanifolds in Products of Non-Positively Curved Manifolds. https://arxiv.org/abs/2604.01415

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