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Licensed Unlicensed Requires Authentication Published by De Gruyter May 5, 2015

Non-existence of certain Einstein metrics on some symplectic manifolds

Augustin Banyaga and Fortuné Massamba
From the journal Forum Mathematicum


We present a necessary and sufficient condition for an Einstein metric on a symplectic manifold (M,ω) to be ω-compatible. An immediate consequence of the solution of the Goldberg conjecture by Sekigawa is that there exists no Einstein metric with non-negative Ricci curvature satisfying our condition on compact symplectic manifolds that admit no Kähler structure.

MSC: 53C25; 53D05

The first named author would like to thank the Department of Mathematics of the University of Botswana for its hospitality and support during the preparation of this paper. The authors also thank the referee for helping them improve the presentation.

Received: 2013-12-31
Revised: 2014-10-11
Published Online: 2015-5-5
Published in Print: 2016-5-1

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