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 \(\mathrm {Spin}\)-manifold have many non-trivial homotopy groups provided that the manifold admits such a metric.

中文翻译：

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正中间曲率度量的空间

在本文中，我们研究了具有中间曲率下界的黎曼度量空间。我们表明，在给定的高维\(\mathrm {Spin}\)流形上，正p曲率和k正Ricci 曲率的度量空间具有许多非平凡同伦群，前提是流形允许这样的度量.