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K-spaces of maximal rank

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We consider a special type of K-space, i.e., almost-Hermitian manifolds whose fundamental form is a Killing form. The K-spaces of this type are characterized by the fact that their dimension is equal to the rank of the covariant derivative of the structure form. A number of the properties of such spaces are established (they are Einstein, compact, have finite fundamental group, etc.). It is proved that every K-space is locally equivalent to a product of a K-space of maximal rank and a Kähler manifold. The K-spaces with zero holomorphic sectional curvature are studied.

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Translated from Matematicheskie Zametki, Vol. 22, No. 4, pp. 465–476, October, 1977.

In conclusion, I thank A. M. Vasil'ev for his constant interest and assistance.

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Kirichenko, V.F. K-spaces of maximal rank. Mathematical Notes of the Academy of Sciences of the USSR 22, 751–757 (1977). https://doi.org/10.1007/BF01146417

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  • Manifold
  • Structure Form
  • Covariant Derivative
  • Fundamental Group
  • Sectional Curvature