Geometric Realizability of Covariant Derivative K\"ahler Tensors for almost Pseudo-Hermitian and almost Para-Hermitian Manifolds

Abstract

The covariant derivative of the K\"ahler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which satisfies these algebraic relations can be realized geometrically.