Matematicheskie Zametki
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

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

$K$-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.

Full text: PDF file (987 kB)

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

Bibliographic databases:

UDC: 513.7

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} 

• http://mi.mathnet.ru/eng/mz8067
• http://mi.mathnet.ru/eng/mz/v22/i4/p465

 SHARE:

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
2. V. F. Kirichenko, “Quasihomogeneous manifolds and generalized almost-Hermitian structures”, Math. USSR-Izv., 23:3 (1984), 473–486
3. V. F. Kirichenko, N. N. Shchipkova, “On the geometry of Gray–Vaisman manifolds”, Russian Math. Surveys, 49:2 (1994), 161–162
4. L. A. Ignatochkina, V. F. Kirichenko, “Conformally invariant properties of approximately Kählerian manifolds”, Math. Notes, 66:5 (1999), 541–549
5. Oleg Mushkarov, “Partially integrable almost complex structures”, Proc. Steklov Inst. Math., 311 (2020), 214–224
•  Number of views: This page: 160 Full text: 70 First page: 1