Highly connected 7-manifolds and non-negative sectional curvature
Sebastian Goette, Michael J. Kerin, Krishnan Shankar
Abstract
In this article, a six-parameter family of highly connected 7-manifolds which admit an $\mathrm{SO}(3)$-invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an $\mathrm{SO}(3)$-invariant metric of non-negative curvature.
Topics & Concepts
Sectional curvatureMathematicsInvariant (physics)Negative curvatureCurvatureMetric (unit)Pure mathematicsSimply connected spaceDimension (graph theory)Scalar curvatureGeometryMathematical physicsEconomicsOperations managementGeometric Analysis and Curvature FlowsGeometric and Algebraic TopologyAdvanced Operator Algebra Research