On locally conformal Kähler space forms - Koji Matsumoto (International Journal of Mathematics and Mathematical Sciences)
An m-dimensional locally conformal Kähler manifold (l.c.K-manifold) is characterized as a Hermitian manifold admitting a global closed l-form αλ (called the Lee form) whose structure (Fμλ,gμλ) satisfies ∇νFμλ=−βμgνλ+βλgνμ−αμFνλ+αλFνμ, where ∇λ denotes the covariant differentiation with respect to the Hermitian metric gμλ, βλ=−Fλϵαϵ, Fμλ=Fμϵgϵλ and the indices ν,μ,…,λ run over the range 1,2,…,m.