Nearly Kähler manifolds with vanishing Tricerri–Vanhecke Bochner curvature tensor

• Published in: Differential geometry and its applications Vol. 27; no. 2; pp. 250 - 256
• Main Authors: Euh, Y., Park, J.H., Sekigawa, K.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-04-2009
• Subjects: Bochner flat manifold; Conformally flat manifold; Curvature tensor; Nearly Kähler manifold; Conformally flat manifold; Curvature tensor; 53C15; 53C55; Nearly Kähler manifold; Bochner flat manifold
• ISSN: 0926-2245; 1872-6984
• DOI: 10.1016/j.difgeo.2008.10.007

We study the local structures of nearly Kähler manifolds with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke (TV). We show that there does not exist a TV Bochner flat strict nearly Kähler manifold in
2
n
(
⩾
10
)
dimension and determine the local structures of the manifolds in 6 and 8 dimensions.