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Canonical almost-Kähler metrics dual to general plane-fronted wave Lorentzian metrics

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In the compact setting, Aazami and Ream (Lett Math Phys 112(4):17, 2002) proved that Riemannian metrics dual to a class of Lorentzian metrics, called (compact) general plane-fronted waves, are almost-Kähler. In this note, we explain how to construct extremal and second-Chern–Einstein non-Kähler almost-Kähler metrics dual to those general plane-fronted waves.

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Authors and Affiliations

  1. Department of Mathematics, Bronx Community College of CUNY, Bronx, NY, 10453, USA

    Mehdi Lejmi

  2. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    Xi Sisi Shen

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  1. Mehdi Lejmi
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  2. Xi Sisi Shen
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Correspondence to Mehdi Lejmi.

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The authors are warmly grateful to Amir Babak Aazami for giving his insights on pp-wave spacetimes and his comments on the note. The authors are also thankful to Daniele Angella, Giuseppe Barbaro, Abdellah Lahdili and Ali Maalaoui for very useful discussions. The first author is supported by the Simons Foundation Grant #636075.

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Lejmi, M., Shen, X.S. Canonical almost-Kähler metrics dual to general plane-fronted wave Lorentzian metrics. Math. Z. 303, 94 (2023). https://doi.org/10.1007/s00209-023-03254-1

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