 On locally conformal Kähler space formsKoji Matsumoto International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-6 Abstract: 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. Date: 1985 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:569581 DOI: 10.1155/S0161171285000060 Access Statistics for this article More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi |
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