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- W2501924703 abstract "The present paper is devoted to the study of differential geometry of Kaehlerian homogeneous spaces. In section 1 we deal with the canonical decomposition of a simply connected complete Kaehlerian space and that of its largest connected group of automorphisms. We know that a simply connected complete Riemannian space V is the product of Riemannian spaces V 0 , V 1 , …, V n , where V 0 is a Euclidean space and V 1 , …, V n are not locally flat and their homogeneous holonomy groups are irreducible [2]. Moreover, if V is homogeneous, so are all V k [10]. We shall show that if V is Kaehlerian space with real analytic metric (resp. Kaehlerian homogeneous space), each factor V k is also Kaehlerian (resp. Kaehlerian homogeneous) and that V is the product of V 0 , V 1 , …, V n as Kaehlerian space. We call this decomposition the de Rham decomposition of the Kaehlerian space V . Although this result is supposedly known, there is no published proof as yet. Using this decomposition theorem we shall show that the largest connected group of automorphisms of a simply connected complete Kaehlerian space with real analytic metric is the direct product of those of the factors of the de Rham decomposition. In the Riemannian case this result has be been established in [3] by one of the authors of the present paper." @default.
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- W2501924703 date "1957-02-01" @default.
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- W2501924703 title "Some Studies on Kaehlerian Homogeneous Spaces" @default.
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- W2501924703 doi "https://doi.org/10.1017/s0027763000001963" @default.
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