A note on canonical Ricci forms on 2-step nilmanifolds

Vezzoni, Luigi

doi:10.1090/S0002-9939-2012-11501-1

A note on canonical Ricci forms on $2$-step nilmanifolds
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Proc. Amer. Math. Soc. 141 (2013), 325-333 Request permission

Abstract:

In this paper 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 (i.e. $d^*\omega =0$).

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