Flat degenerate metrics and Riemannian foliations

Brice Flamencourt

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arXiv · 2501.16593

Flat degenerate metrics and Riemannian foliations

Brice Flamencourt

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Abstract

Bandyopadhyay, Dacorogna, Matveev and Troyanov conjectured that a closed manifold admitting a flat, non-negative definite metric of constant rank $m$ should be finitely covered by a fiber bundle over the $m$-torus. We give a counter-example to this statement and we discuss the link between this problem and the study of transversely flat Riemannian foliations.

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BibTeX RIS

Brice Flamencourt. 2025-01-28. Flat degenerate metrics and Riemannian foliations. https://arxiv.org/abs/2501.16593

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