Einstein almost cok\"ahler manifolds
Abstract
We study an odd-dimensional analogue of the Goldberg conjecture for compact Einstein almost K\"ahler manifolds. We give an explicit non-compact example of an Einstein almost cok\"ahler manifold that is not cok\"ahler. We prove that compact Einstein almost cok\"ahler manifolds with non-negative -scalar curvature are cok\"ahler (indeed, transversely Calabi-Yau); more generally, we give a lower and upper bound for the -scalar curvature in the case that the structure is not cok\"ahler. We prove similar bounds for almost K\"ahler Einstein manifolds that are not K\"ahler.
Cite
@article{arxiv.1409.4437,
title = {Einstein almost cok\"ahler manifolds},
author = {Diego Conti and Marisa Fernández},
journal= {arXiv preprint arXiv:1409.4437},
year = {2016}
}
Comments
18 pages; v2, corrected statement and proof of main theorem, added Theorem 4.2 for comparison with even-dimensional case, added two references, improved presentation; v3, added Lemma 4.1 for completeness, improved presentation. To appear in Mathematische Nachrichten