In this paper we study the static Einstein–Maxwell space when it is conformal to an n-dimensional pseudo-Euclidean space, which invariant under action of $$(n-1)$$ -dimensional translation group. We also provide a complete classification such space.

The Alesker product turns the space of smooth translation-invariant valuations on convex bodies into a commutative associative unital algebra, satisfying Poincaré duality and hard Lefschetz theorem. In this article, version Hodge-Riemann relations for algebra is conjectured, conjecture proved in two particular situations: even valuations, 1-homogeneous valuations. latter result then used to ded...