Flats in 3-manifolds
نویسنده
چکیده
— We prove that if a closed aspherical Riemannian 3-manifold M contains a 2-flat, then there exists a free abelian subgroup of rank two in π1(M). Under some restrictions on the topology of M we prove the existence of an immersed incompressible flat torus in M . This generalizes results which were previously known for manifolds of nonpositive curvature. RÉSUMÉ. — Nous prouvons que si une variété riemannienne fermée de dimension trois M contient un 2-plat, alors il existe un sous-groupe abélien libre de rang 2 dans π1(M). Sous certaines restrictions sur la topologie de M , nous prouvons l’existence d’un tore plat incompressible dans M . Ceci généralise des résultats connus au préalable pour des variétés de courbure non positive.
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تاریخ انتشار 1998