Abstract
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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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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DOI: https://doi.org/10.1007/s00209-023-03254-1
Keywords
- Extremal almost-Kähler Metrics
- Second-Chern–Einstein almost-Kähler metrics
- Lorentzian metrics
- pp-wave spacetimes