Mathematical Research Letters

Volume 23 (2016)

Number 5

Quaternionic contact Einstein manifolds

Pages: 1405 – 1432

DOI: http://dx.doi.org/10.4310/MRL.2016.v23.n5.a8

Authors

Stefan Ivanov (Faculty of Mathematics and Informatics, University of Sofia, Bulgaria; and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences)

Ivan Minchev (Faculty of Mathematics and Informatics, University of Sofia, Bulgaria; and Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic)

Dimiter Vassilev (Department of Mathematics and Statistics, University of New Mexico, Albuquerque, N.M., U.S.A.)

Abstract

We show that a seven dimensional quaternionic contact Einstein manifold has constant qc-scalar curvature. In addition, we characterize qc-Einstein structures with certain flat vertical connection and develop their local structure equations. Finally, regular qc-Ricci flat structures are shown to fiber over hyper-Kähler manifolds.

Keywords

quaternionic contact structures, qc-conformal flatness, qc-conformal curvature, Einstein structures

2010 Mathematics Subject Classification

53C17

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Published 12 January 2017