A Wick-rotatable metric is purely electric
arXiv:1504.01244
Abstract
We show that a metric of arbitrary dimension and signature which allows for a standard Wick-rotation to a Riemannian metric necessarily has a purely electric Riemann and Weyl tensor.
9 pages, v2:changed and tighten proof. Slightly changed in order to be compatible with the definitions of Wick-rotations in arxiv:1703.04576 [math.DG]