# Compact manifolds with positive [formula omitted]-curvature

- Authors
- Journal
- Differential Geometry and its Applications 0926-2245
- Publisher
- Elsevier
- Identifiers
- DOI: 10.1016/j.difgeo.2014.09.002
- Keywords

## Abstract

Abstract The Schouten tensor A of a Riemannian manifold (M,g) provides the important σk-scalar curvature invariants, that are the symmetric functions in the eigenvalues of A, where, in particular, σ1 coincides with the standard scalar curvature Scal(g). Our goal here is to study compact manifolds with positive Γ2-curvature, i.e., when σ1(g)>0 and σ2(g)>0. In particular, we prove that a 3-connected non-string manifold M admits a positive Γ2-curvature metric if and only if it admits a positive scalar curvature metric. Also we show that any finitely presented group π can always be realised as the fundamental group of a closed manifold of positive Γ2-curvature and of arbitrary dimension greater than or equal to six.

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