An m -dimensional locally conformal Kähler manifold (l.c.K-manifold) is characterized as a Hermitian manifold admitting a global closed l -form α λ (called the Lee form) whose structure ( F μ λ , g μ λ ) satisfies ∇ ν F μ λ = − β μ g ν λ + β λ g ν μ − α μ F ν λ + α λ F ν μ , where ∇ λ denotes the covariant differentiation with respect to the Hermitian metric g μ λ , β λ = − F λ ϵ α ϵ , F μ λ = F μ ϵ g ϵ λ and the indices ν , μ , … , λ run over the range 1 , 2 , … , m .

For l. c. K-manifolds, I. Vaisman [4] gave a typical example and T. Kashiwada ([1], [2],[3]) gave a lot of interesting properties about such manifolds.

In this paper, we shall study certain properties of l. c. K-space forms. In § 2 , we shall mainly get the necessary and sufficient condition that an l. c. K-space form is an Einstein one and the Riemannian curvature tensor with respect to g μ λ will be expressed without the tensor field P μ λ . In § 3 , we shall get the necessary and sufficient condition that the length of the Lee form is constant and the sufficient condition that a compact l. c. K-space form becomes a complex space form. In the last § 4 , we shall prove that there does not exist a non-trivial recurrent l. c. K-space form.