佐々木多様体における半対称計量φ-接続
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概要
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In previous papers the author has proved two following theorems. 1) If the Kaehlerian manifold has a constant holomorphic sectional curvature k at each point of the manifold with respect to a special semi-symmetric metric F-connection, then the Bochner curvature tensor of the Kaehlerian manifold vanishes. [3] 2) If a Kaehlerian manifold of dimension n≧4 admits a special semi-symmetric metric F-connection in the sense of the present section such that the tortion tensor S^h_<ji> satisfies D_kS^h_<ji>=0 and the curvature tensor R^h_<kji> is of the form R^h_<kji>=α_<kj>F^h_i, then the manifold is of a constant holmorphic sectional curvature. [1] In the present paper the author tries to study analogous properties in a Sasakian manifold.