On the existence of balanced and SKT metrics on nilmanifolds

By Anna Fino, Luigi Vezzoni. 2015

72 citations recorded by the source corpus.

On a complex manifold an Hermitian metric which is simultaneously SKT and balanced has to be necessarily K\"ahler. It has been conjectured that if a compact complex manifold (M,J) has an SKT metric and a balanced metric both compatible with J, then (M, J) is necessarily K\"ahler. We show that the conjecture is true for nilmanifolds.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4506e0db353a44fd7e1e9e8d4bbe6d475b07ecbd

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Balanced Hermitian structures on almost abelian Lie algebras (2020, background): “This has been confirmed on some special classes of compact complex manifolds: twistor spaces of compact anti-self-dual Riemannian manifolds [56], non-Kähler manifolds belonging to the Fujiki class C [15], a family of non-Kähler Calabi-Yau threefolds constructed in [31], generalized Calabi-Gray manif”
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.”