Spaces of positive intermediate curvature metrics

Abstract

In this paper we study spaces of Riemannian metrics with lower bounds on intermediate curvatures. We show that the spaces of metrics of positive p-curvature and k-positive Ricci curvature on a given high-dimensional Spin-manifold have many non-trivial homotopy groups provided that the manifold admits such a metric.

Positive $(p, n)$-intermediate scalar curvature and cobordism

“…During the writing of this paper we discovered that Theorem B also follows as a case of a recent theorem of Frenck and Kordass [15]. Their work extends some powerful techniques of [2], for positive scalar curvature to the cases of positive pp, nq-intermediate scalar curvature and also positive k-Ricci curvature; see Theorems A and B of [15].…”

“…During the writing of this paper we discovered that Theorem B also follows as a case of a recent theorem of Frenck and Kordass [15]. Their work extends some powerful techniques of [2], for positive scalar curvature to the cases of positive pp, nq-intermediate scalar curvature and also positive k-Ricci curvature; see Theorems A and B of [15]. Our work has independent value, as Theorem A above provides a geometrically explicit construction of an s p,n ą 0 metric over the trace of an appropriate surgery, something which is not done in [15].…”

“…Their work extends some powerful techniques of [2], for positive scalar curvature to the cases of positive pp, nq-intermediate scalar curvature and also positive k-Ricci curvature; see Theorems A and B of [15]. Our work has independent value, as Theorem A above provides a geometrically explicit construction of an s p,n ą 0 metric over the trace of an appropriate surgery, something which is not done in [15]. In doing so, we also provide detailed curvature calculations for sectional and intermediate scalar curvature of various warped product metrics that are of value in their own right.…”