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arXiv · 1409.4437

Einstein almost cok\"ahler manifolds

Diego Conti·Marisa Fernández
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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.

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Diego Conti, Marisa Fernández. 2014-09-15. Einstein almost cok\"ahler manifolds. https://arxiv.org/abs/1409.4437

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