Spaces of constant almost holomorphic curvature

Abstract

In this work, special pseudo-Riemannian spaces endowed with an affinor structure satisfying certain naturally arising conditions are investigated. Spaces with a special form of the Riemann tensor are considered, and two types of pseudo-Riemannian spaces are distinguished depending on the type of their Riemann tensor. Their geometric characteristics are obtained for a specific form of the metric tensor. In particular, it is proven that pseudo-Riemannian spaces of constant almost holomorphic curvature with an elliptic skew-symmetric affinor structure of second degree are semi-symmetric. The research is carried out locally, using tensor methods without imposing restrictions on the signature or definiteness of the metric tensor of the space under consideration. A special conjugation operation, introduced for spaces endowed with an affinor structure, is widely applied, along with its properties for the Riemann and Ricci tensors.