Nearly Kähler manifolds with vanishing Tricerri-Vanhecke Bochner curvature tensor
The authors give a local classification of nearly Kähler manifolds \((M,g,J)\) with vanishing Tricieri-Vanhecke (TV) curvature Bochner type tensor \(B(R)\). For Kähler manifolds the tensor \(B(R)\) coincides with the Bochner tensor. The authors prove that there do not exist TV Bochner flat strict nearly Kähler manifolds of dimension \(2n\geq 10\). The main result of the paper is the following theorem: Theorem. Let \((M,g,J)\) be a \(2n\geq 6\)-dimensional TV Bochner flat strict nearly Kähler manifold. Then \(M\) is either a 6-dimensional space of positive constant sectional curvature or locally a product of 6-dimensional strict nearly Kähler manifold of positive constant sectional curvature \(K\) and a Riemannian surface of constant Gaussian curvature \(-K\).
scientific article; zbMATH DE number 5544184
scientific article