This article is cited in 10 papers

$K$-spaces of maximal rank

V. F. Kirichenko

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 513.7

Received: 12.03.1975

 English version: Mathematical Notes, 1977, 22:4, 751–757

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