Kaehler and para-Kaehler curvature Weyl manifolds

2010/11/22 by Gilkey, Peter, Nikcevic, Stana
#53B05 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1011.4844

Abstract

We show that the Weyl structure of an almost-Hermitian Weyl manifold of dimension at least 6 is trivial if the associated curvature operator satisfies the Kaehler identity. Similarly if the curvature of an almost para-Hermitian Weyl manifold of dimension at least 6 satisfies the para-Kaehler identity, then the Weyl structure is trivial as well.

Related

• (para)-Kähler Weyl structures
• 4-dimensional (para)-Kähler--Weyl structures
• Algebraic reduction of certain almost Kaehler manifolds
• The structure of AK₂-manifolds
• A Kaehler Einstein structure on the cotangent bundle of a Riemannian manifold