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- Title
Curvature of quaternionic Kähler manifolds with S1-symmetry.
- Authors
Cortés, V.; Saha, A.; Thung, D.
- Abstract
We study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic Kähler side in terms of the initial hyper-Kähler data. Our curvature formula refines a well-known decomposition theorem due to Alekseevsky. As an application, we compute the norm of the curvature tensor for a series of complete quaternionic Kähler manifolds arising from flat hyper-Kähler manifolds. We use this to deduce that these manifolds are of cohomogeneity one.
- Publication
Manuscripta Mathematica, 2022, Vol 168, Issue 1/2, p35
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/s00229-021-01294-7