Positive intermediate Ricci curvature on products of homogeneous spaces

Abstract

We establish metrics of positive $2^{\mathrm{nd}}$-intermediate Ricci curvature, i.e. ${\mathrm{Ric}}_2>0$, on products of positively curved homogeneous spaces. Using these examples, we demonstrate that the Hopf conjectures, Petersen-Wilhelm conjecture, Berger fixed point theorem, and Hsiang-Kleiner theorem for positively curved manifolds do not hold in the ${\mathrm{Ric}}_2>0$ setting. These observations indicate that the class of manifolds with ${\mathrm{Ric}}_2>0$ is vastly different from the class of positively curved manifolds.

arXiv commentSubmission withdrawn because there is a mistake in Lemma 4.5, meaning the main result (Theorem 4.1) is incorrect

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• Focal Radius, Rigidity, and Lower Curvature Bounds
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Cited by in corpus (1)

• Local symmetry rank bound for positive intermediate Ricci curvatures