A note on Canonical Ricci forms on 2-step nilmanifolds

Abstract

In this note we prove that any left-invariant almost Hermitian structure on a 2-step nilmanifold is Ricci-flat with respect to the Chern connection and that it is Ricci-flat with respect to another canonical connection if and only if it is cosymplectic.

7 pages. Typos corrected. To appear in Proc. of the AMS

References in corpus (2)

• Almost Hermitian Geometry on Six Dimensional Nilmanifolds
• Quasi-Kähler manifolds with trivial Chern Holonomy