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Fundam. Prikl. Mat., 2002, Volume 8, Issue 2, Pages 357–364 (Mi fpm650)  

This article is cited in 3 scientific papers (total in 3 papers)

On the type number of nearly-cosymplectic hypersurfaces in nearly-Kählerian manifolds

M. B. Banaru

Moscow State Pedagogical University

Abstract: Nearly-cosymplectic hypersurfaces in nearly-Kählerian manifolds are considered. The following results are obtained.
Theorem 1. The type number of a nearly-cosymplectic hypersurface in a nearly-Kählerian manifold is at most one.
Theorem 2. Let $\sigma$ be the second fundamental form of the immersion of a nearly-cosymplectic hypersurface $(N,\{\Phi,\xi,\eta,g\})$ in a nearly-Kählerian manifold $M^{2n}$. Then $N$ is a minimal submanifold of $M^{2n}$ if and only if $\sigma(\xi,\xi)=0$.
Theorem 3. Let $N$ be a nearly-cosymplectic hypersurface in a nearly-Kählerian manifold $M^{2n}$, and let $T$ be its type number. Then the following statements are equivalent: 1) $N$ is a minimal submanifold of $M^{2n}$; 2) $N$ is a totally geodesic submanifold of $M^{2n}$; 3) $T\equiv0$.

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Bibliographic databases:
UDC: 513.82
Received: 01.03.2002

Citation: M. B. Banaru, “On the type number of nearly-cosymplectic hypersurfaces in nearly-Kählerian manifolds”, Fundam. Prikl. Mat., 8:2 (2002), 357–364

Citation in format AMSBIB
\Bibitem{Ban02}
\by M.~B.~Banaru
\paper On the type number of nearly-cosymplectic hypersurfaces in nearly-K\"ahlerian manifolds
\jour Fundam. Prikl. Mat.
\yr 2002
\vol 8
\issue 2
\pages 357--364
\mathnet{http://mi.mathnet.ru/fpm650}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1939251}
\zmath{https://zbmath.org/?q=an:1036.53013}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. B. Banaru, “On the Kenmotsu hypersurfaces of special Hermitian manifolds”, Siberian Math. J., 45:1 (2004), 7–10  mathnet  crossref  mathscinet  zmath  isi  elib
    2. M. B. Banaru, “Almost contact metric hypersurfaces with type number $0$ or $1$ in nearly-Kählerian manifolds”, Moscow University Mathematics Bulletin, 69:3 (2014), 132–134  mathnet  crossref  mathscinet
    3. I. A. Petrov, “Stroenie pochti ermitovykh struktur totalnogo prostranstva glavnogo $T^1$-rassloeniya s ploskoi svyaznostyu nad nekotorymi klassami pochti kontaktnykh metricheskikh mnogoobrazii”, Chebyshevskii sb., 18:2 (2017), 183–194  mathnet  crossref  mathscinet  elib
  • Фундаментальная и прикладная математика
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