On the non-Riemannian quantity H of an (α,β)(α,β)-metric

In this article, first we compute H  -curvature of (α,β)(α,β)-metrics, when β   is a closed 1-form. Next, we apply this formula to discuss some special (α,β)(α,β)-metrics and we obtain necessary and sufficient conditions for these metrics to have almost vanishing H  -curvature. Moreover we characterize Einstein square metric F=(α+β)2α, when β is a closed 1-form and in this case it is proven that it has vanishing H-curvature.