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Mat. Zametki, 1977, Volume 22, Issue 4, Pages 465–476 (Mi mz8067)  

This article is cited in 5 scientific papers (total in 5 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.

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

Bibliographic databases:

UDC: 513.7
Received: 12.03.1975

Citation: V. F. Kirichenko, “$K$-spaces of maximal rank”, Mat. Zametki, 22:4 (1977), 465–476; Math. Notes, 22:4 (1977), 751–757

Citation in format AMSBIB
\Bibitem{Kir77}
\by V.~F.~Kirichenko
\paper $K$-spaces of maximal rank
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 4
\pages 465--476
\mathnet{http://mi.mathnet.ru/mz8067}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=474103}
\zmath{https://zbmath.org/?q=an:0361.53024}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 4
\pages 751--757
\crossref{https://doi.org/10.1007/BF01146417}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. F. Kirichenko, “The geometry of $T$-recurrent manifolds”, Russian Math. Surveys, 38:1 (1983), 196–197  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. F. Kirichenko, “Quasihomogeneous manifolds and generalized almost-Hermitian structures”, Math. USSR-Izv., 23:3 (1984), 473–486  mathnet  crossref  mathscinet  zmath
    3. V. F. Kirichenko, N. N. Shchipkova, “On the geometry of Gray–Vaisman manifolds”, Russian Math. Surveys, 49:2 (1994), 161–162  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. L. A. Ignatochkina, V. F. Kirichenko, “Conformally invariant properties of approximately Kählerian manifolds”, Math. Notes, 66:5 (1999), 541–549  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Oleg Mushkarov, “Partially integrable almost complex structures”, Proc. Steklov Inst. Math., 311 (2020), 214–224  mathnet  crossref  crossref  isi  elib
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