Topological obstructions to nonnegative scalar curvature and mean convex boundary

2018/11/20 by Barbosa, Ezequiel, Conrado, Franciele
#53C21 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.08519

Abstract

We study topological obstructions to the existence of a Riemannian metric on manifolds with boundary such that the scalar curvature is non-negative and the boundary is mean convex. We construct many compact manifolds with boundary which admit no Riemannian metric with non-negative scalar curvature and mean convex boundary. For example, we show that the manifold (T^n-2× Σ)# N, where Σ is a compact, connected and orientable surface which is not a disk or a cylinder and N is a closed n-dimensional manifold, does not admit a metric of non-negative scalar curvature and mean convex boundary, and the manifold (I× T^n-1)#N, where I=[a,b], does not admit a metric of positive scalar curvature and mean convex boundary.

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