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Mat. Zametki, 1976, Volume 19, Issue 5, Pages 805–814 (Mi mz7801)  

This article is cited in 8 scientific papers (total in 8 papers)

$K$-spaces of constant holomorphic sectional curvature

V. F. Kirichenko

M. V. Lomonosov Moscow State University

Abstract: In this note we prove the equivalence of the pointwise constancy and the global constancy of the holomorphic sectional curvature of a $K$-space. A criterion for the constancy of the holomorphic sectional curvature of a $K$-space is found. It is proved that every proper $K$-space of constant holomorphic sectional curvature is a six-dimensional orientable Riemannian manifold of constant positive curvature, which is isometric with the six-dimensional sphere in the case of completeness and connectedness.

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English version:
Mathematical Notes, 1976, 19:5, 473–478

Bibliographic databases:

UDC: 513.7
Received: 04.11.1974

Citation: V. F. Kirichenko, “$K$-spaces of constant holomorphic sectional curvature”, Mat. Zametki, 19:5 (1976), 805–814; Math. Notes, 19:5 (1976), 473–478

Citation in format AMSBIB
\Bibitem{Kir76}
\by V.~F.~Kirichenko
\paper $K$-spaces of constant holomorphic sectional curvature
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 5
\pages 805--814
\mathnet{http://mi.mathnet.ru/mz7801}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=425862}
\zmath{https://zbmath.org/?q=an:0337.53038|0333.53030}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 5
\pages 473--478
\crossref{https://doi.org/10.1007/BF01142574}


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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, “Locally conformallity Kählerian manifolds of constant holomorphic sectional curvature”, Math. USSR-Sb., 72:2 (1992), 333–342  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. O. E. Arsen'eva, “Conformally half-planar generalized Kähler manifolds”, Russian Math. Surveys, 47:4 (1992), 199–200  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. O. E. Arsen'eva, “Selfdual geometry of generalized Kählerian manifolds”, Russian Acad. Sci. Sb. Math., 79:2 (1994), 447–457  mathnet  crossref  mathscinet  zmath  isi
    4. V. F. Kirichenko, L. V. Stepanova, “The geometry of hypersurfaces of quasi-Kählerian manifolds”, Russian Math. Surveys, 50:2 (1995), 440–441  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. 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
    6. V. F. Kirichenko, L. I. Vlasova, “Concircular geometry of nearly Kähler manifolds”, Sb. Math., 193:5 (2002), 685–707  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. B. V. Zayatuev, “On a Class of Almost-Hermitian Structures on Tangent Bundles”, Math. Notes, 76:5 (2004), 682–688  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. V. F. Kirichenko, E. V. Kusova, “On geometry of weakly cosymplectic manifolds”, J. Math. Sci., 177:5 (2011), 668–674  mathnet  crossref  mathscinet  elib
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