Four-dimensional almost Hermitian manifolds with vanishing Tricerri-Vanhecke Bochner curvature tensor

TL;DR

This paper investigates four-dimensional almost Hermitian manifolds with zero Tricerri-Vanhecke Bochner curvature tensor, providing local structure theorems and examples for such manifolds, especially in the Kähler case.

Contribution

It offers new local structure theorems and explicit examples for four-dimensional almost Hermitian manifolds with vanishing Tricerri-Vanhecke Bochner curvature tensor.

Findings

Derived local structure theorems for these manifolds

Constructed explicit examples related to the theorems

Enhanced understanding of curvature properties in this class

Abstract

We study curvature properties of four-dimensional almost Hermitian manifolds with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. We give local structure theorems for such Kaehler manifolds, and find out several examples related to the theorems.