A correction to “Tamed symplectic forms and strong Kähler with torsion metrics”
By Nicola Enrietti, Anna Fino, Luigi Vezzoni. The Journal of Symplectic Geometry, 2012
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Proof of Theorem 1.3. Let (M = G/Γ, J) be a nilmanifold with an invariant complex structure and let (g, J) be its Lie algebra. Assume that there exists a Hermitian-symplectic structure Ω on (M,J). Using Lemma 3.2 in [2], we may assume that Ω is left-invariant. Hence, Ω can be regarded as a Hermitian-symplectic structure on (g, J). Using Proposition 2.1 in [2], we have that Ω induces an SKT inner product on (g, J). Since g is nilpotent but non abelian, there exists a non-zero vector in the intersection of the center ξ and the commutator g1 = [g, g]. Since the center ξ is J-invariant, then Jξ ∩ g1 6= {0} and Theorem 1.1 in [2] implies the statement.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/138440359c6ae640686cfef4a4dd824550a405d5
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Citations in the corpus
- Strominger connection and pluriclosed metrics (2019, background): “, we refer the readers to [1], [7], [11], [17], [20], [23], [24], [27], [28], [29], [37], [38], [40], [44], [49] and the references therein for more discussions and backgrounds.”