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The Lebrun--Salamon conjecture is true in dimension up to 56
We prove the LeBrun--Salamon conjecture for positive quaternionic Kähler manifolds of quaternionic dimension n <= 14. To do so, we first show that the isometry group Isom(M) of any minimal counterexample M has rank at most one, hence dimension at most three. On the other hand, we consider a characte
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