Special Hermitian metrics on Oeljeklaus-Toma manifolds

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Oeljeklaus–Toma (OT) manifolds are higher dimensional analogues of Inoue-Bombieri surfaces and their construction is associated to a finite extension (Formula presented.) of (Formula presented.) and a subgroup of units (Formula presented.). We characterize the existence of pluriclosed metrics (also known as strongly Kähler with torsion (SKT) metrics) on any OT manifold (Formula presented.) purely in terms of number-theoretical conditions, yielding restrictions on the third Betti number (Formula presented.) and the Dolbeault cohomology group (Formula presented.). Combined with the main result in (Dubickas, Results Math. 76 (2021), 78), these numerical conditions render explicit examples of pluriclosed OT manifolds in arbitrary complex dimension. We prove that in complex dimension 4 and type (Formula presented.), the existence of a pluriclosed metric on (Formula presented.) is entirely topological, namely, it is equivalent to (Formula presented.). Moreover, we provide an explicit example of an OT manifold of complex dimension 4 carrying a pluriclosed metric. Finally, we show that no OT manifold admits balanced metrics, but all of them carry instead locally conformally balanced metrics.

TidsskriftBulletin of the London Mathematical Society
Sider (fra-til)655
Antal sider667
StatusUdgivet - 22 mar. 2022
Udgivet eksterntJa


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