Abstract
Scalar curvature is the simplest generalization of Gaussian curvature to higher dimensions. However there are many questions open with regard to its relation to other geometric quantities and topology. Here we will prove and illustrate some features of scalar curvature in higher dimensions related to a general hammock effect for scalar curvature, namely the one-sided affinity for curvature decreasing deformations. The first one is concerned with some prescribed decrease of the scalar curvature Scal(g) of some Riemannian metric g on a given manifoldMn of dimension≥ 3. We denote the e−neighborhood of some set U with respect to g by Ue.
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