Author:
Cortés V.,Saha A.,Thung D.
Abstract
AbstractWe 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.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Reference15 articles.
1. Alekseevsky, D.V., Cortés, V., Dyckmanns, M., Mohaupt, T.: Quaternionic Kähler metrics associated with special Kähler manifolds. J. Geom. Phys. 92, 271–87 (2015)
2. Alekseevsky, D.V., Cortés, V., Mohaupt, T.: Conification of Kähler and hyper-Kähler manifolds. Commun. Math. Phys. 324, 637–55 (2013)
3. Alekseevsky, D.V.: Riemannian spaces with unusual holonomy groups. Funkt. Anal. Priloz. 2, 1–10 (1968)
4. Alexandrov, S., Persson, D., Pioline, B.: Wall-crossing, Rogers Dilogarithm, and the QK/HK correspondence. J. High Energy Phys. 1112, 027 (2011)
5. Cortés, V., Dyckmanns, M., Jüngling, M., Lindemann, D.: A class of cubic hypersurfaces and quaternionic Kähler manifolds of co-homogeneity one. arXiv:1701.07882 [math.DG]. To appear in Asian J. Math. Accepted (March 13, 2020)
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