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A note on canonical Ricci forms on $ 2$-step nilmanifolds


Author: Luigi Vezzoni
Journal: Proc. Amer. Math. Soc. 141 (2013), 325-333
MSC (2000): Primary 53C15; Secondary 53B15
DOI: https://doi.org/10.1090/S0002-9939-2012-11501-1
Published electronically: May 7, 2012
MathSciNet review: 2988734
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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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Additional Information

Luigi Vezzoni
Affiliation: Dipartimento di Matematica, Università di Torino, Torino, Italy
Email: luigi.vezzoni@unito.it

DOI: https://doi.org/10.1090/S0002-9939-2012-11501-1
Received by editor(s): June 8, 2011
Published electronically: May 7, 2012
Additional Notes: The author was supported by the Project M.I.U.R. “Riemannian Metrics and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M.
Communicated by: Lei Ni
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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