A remark on the Bismut-Ricci form on 2-step nilmanifolds

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 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.

5 pages. Comments are welcome

Cited by in corpus (5)

• The long-time behavior of the homogeneous pluriclosed flow
• Hermitian Curvature flow on unimodular Lie groups and static invariant metrics
• The Hull-Strominger system and the Anomaly flow on a class of solvmanifolds
• Hermitian curvature flow on complex locally homogeneous surfaces
• The Anomaly flow on nilmanifolds