In this note, we observe that, on a 2-step nilpotent Lie group equipped with a left-invariant SKT structure, the (1,1)-part of the Bismut–Ricci form is seminegative definite. As an application, we give a simplified proof of the non-existence of invariant SKT static metrics on 2-step nilmanifolds and of the existence of a long-time solution to the pluriclosed flow in 2-step nilmanifolds.
A remark on the Bismut–Ricci form on 2-step nilmanifolds
PUJIA, MATTIA;Vezzoni, Luigi
2018-01-01
Abstract
In this note, we observe that, on a 2-step nilpotent Lie group equipped with a left-invariant SKT structure, the (1,1)-part of the Bismut–Ricci form is seminegative definite. As an application, we give a simplified proof of the non-existence of invariant SKT static metrics on 2-step nilmanifolds and of the existence of a long-time solution to the pluriclosed flow in 2-step nilmanifolds.
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