Nonpositively curved $4$-manifolds with zero Euler characteristic
| Autor: | Connell, Chris, Ruan, Yuping, Wang, Shi |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show that for any closed nonpositively curved Riemannian 4-manifold $M$ with vanishing Euler characteristic, the Ricci curvature must degenerate somewhere. Moreover, for each point $p\in M$, either the Ricci tensor degenerates or else there is a foliation by totally geodesic flat 3-manifolds in a neighborhood of $p$. As a corollary, we show that if in addition the metric is analytic, then the universal cover of $M$ has a nontrivial Euclidean de Rham factor. Finally we discuss how this result creates an implication of conjectures on simplicial volume in dimension four. Comment: 17 pages |
| Databáze: | arXiv |
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