3-Manifolds with Constant Ricci Eigenvalues (λ, λ, 0)

2021/11/30 by Brooks, Thomas G.
#53C12 #53C20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.15499

Abstract

We consider complete Riemannian 3-manifolds whose Ricci tensors have constant eigenvalues (λ, λ, 0). When π₁ is finitely generated, we classify the topology of such manifolds by showing that they have a free fundamental group if non-trivial and that every free group is obtained. We give a description up to isometry, when the metric is locally irreducible or when it is analytic.

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