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Free Circle Actions and Positive Ricci Curvature on Manifolds with the Cohomology Ring of $S^2\times S^5$

Year: 2026

Type: article

Abstract: We classify which of the 672 oriented diffeomorphism types of closed, simply-connected spin 7-manifolds with the cohomology ring of $S^2\times S^5$ admit a free circle action. In addition, we show that whenever such an action exists, there exist infinitely many pairwise non-equivalent free circle actions. Finally, in almost all cases where such an action exists, we construct invariant Riemannian metrics of positive Ricci curvature.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2026.094

Author: Philipp Reiser

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7147366030

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Cites: 26

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Related to: 10