Riemannian 3-Symmetric Spaces and Homogeneous K-Spaces

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  • Riemannian 3 Symmetric Spaces and Homog

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In the present paper, a Riemannian 3-symmetric space and a homogeneous almost Hermitian manifold are considered in connection with a certain tensor field called a homogeneous structure. An interesting case arises when the manifold is a K-space. Let Μ be a complete and simply connected K-space. It is shown that Μ is a Riemannian 3-symmetric space if and only if Μ is a homogeneous almost Hermitian manifold with homogeneous structure of special Τ̂(X) = 1/2▽ₓJ. Some conditions for the homogeneous structure　be Τ̂ are also considered.

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