Invariant <Emphasis Type="Italic">f</Emphasis>-structures on naturally reductive homogeneous spaces |
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Authors: | V V Balashchenko |
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Institution: | (1) Belarus State University, prosp. Nezavisimosti 4, Minsk, 220050, Republic of Belarus |
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Abstract: | We study invariant metric f-structures on naturally reductive homogeneous spaces and establish their relation to generalized Hermitian geometry. We prove a series of criteria characterizing geometric and algebraic properties of important classes of metric f-structures: nearly Kähler, Hermitian, Kähler, and Killing structures. It is shown that canonical f-structures on homogeneous Φ-spaces of order k (homogeneous k-symmetric spaces) play remarkable part in this line of investigation. In particular, we present the final results concerning canonical f-structures on naturally reductive homogeneous Φ-spaces of order 4 and 5. |
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Keywords: | naturally reductive space invariant f-structure generalized Hermitian geometry homogeneous Φ -space homogeneous k-symmetric space canonical f-structure |
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