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Static SKT metrics on Lie groups

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Abstract

An SKT metric is a Hermitian metric on a complex manifold whose fundamental 2-form ω satisfies \({\partial \overline{\partial} \omega=0}\). Streets and Tian introduced in Streets and Tian (Int Math Res Not IMRN 16:3101–3133, 2010) a Ricci-type flow that preserves the SKT condition. This flow uses the Ricci form associated to the Bismut connection, the unique Hermitian connection with totally skew-symmetric torsion, instead of the Levi-Civita connection. A SKT metric is called static if the (1, 1)-part of the Ricci form of the Bismut connection satisfies (ρ B)(1, 1) = λω for some real constant λ. We study invariant static metrics on simply connected Lie groups, providing in particular a classification in dimension 4 and constructing new examples, both compact and non-compact, of static metrics in any dimension.

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  1. Dipartimento di Matematica G. Peano, Università degli studi di Torino, Via Carlo Alberto 10, 10123, Turin, Italy

    Nicola Enrietti

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  1. Nicola Enrietti
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Correspondence to Nicola Enrietti.

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Enrietti, N. Static SKT metrics on Lie groups. manuscripta math. 140, 557–571 (2013). https://doi.org/10.1007/s00229-012-0552-3

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  • DOI: https://doi.org/10.1007/s00229-012-0552-3

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