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Sibirsk. Mat. Zh., 2003, Volume 44, Number 5, Pages 981–991 (Mi smj1246)  

This article is cited in 9 scientific papers (total in 9 papers)

The type number of the cosymplectic hypersurfaces of 6-dimensional Hermitian submanifolds of the Cayley algebra

M. B. Banaru

Smolensk Humanitarian University

Abstract: We study the 6-dimensional oriented submanifolds of the Cayley algebra which are endowed with the Hermitian structure induced by 3-folds vector cross products. We prove that the type number of a cosymplectic hypersurface of a 6-dimensional Hermitian submanifold of the Cayley algebra is at most 3 and that a 6-dimensional Kaehler submanifold of the octave algebra has no cosymplectic hypersurfaces with the type number greater than one.

Keywords: Cayley algebra, Hermitian manifold, hypersurface, cosymplectic structure, type number

Full text: PDF file (211 kB)
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English version:
Siberian Mathematical Journal, 2003, 44:5, 765–773

Bibliographic databases:

UDC: 513.82
Received: 20.11.2001
Revised: 23.09.2002

Citation: M. B. Banaru, “The type number of the cosymplectic hypersurfaces of 6-dimensional Hermitian submanifolds of the Cayley algebra”, Sibirsk. Mat. Zh., 44:5 (2003), 981–991; Siberian Math. J., 44:5 (2003), 765–773

Citation in format AMSBIB
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\by M.~B.~Banaru
\paper The type number of the cosymplectic hypersurfaces of 6-dimensional Hermitian submanifolds of the Cayley algebra
\jour Sibirsk. Mat. Zh.
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\pages 981--991
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\zmath{https://zbmath.org/?q=an:1080.53048}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 5
\pages 765--773
\crossref{https://doi.org/10.1023/A:1025972300297}
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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. M. B. Banaru, “The Kenmotsu hypersurfaces axiom for $6$-dimensional Hermitian submanifolds of the Cayley algebra”, Siberian Math. J., 55:2 (2014), 210–214  mathnet  crossref  mathscinet  isi
    2. M. B. Banaru, “On almost contact metric hypersurfaces with type number 1 in $6$-dimensional Kählerian submanifolds of Cayley algebra”, Russian Math. (Iz. VUZ), 58:10 (2014), 10–14  mathnet  crossref
    3. Erdogan M., Pirincci B., Alo J., Yilmaz G., “on the Type Number of a Hypersurface in the 6-Dimensional Sphere”, Adv. Geom., 14:4 (2014), 571–578  crossref  mathscinet  zmath  isi  scopus
    4. 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
    5. M. B. Banaru, “The axiom of cosymplectic surfaces and $W_4$-manifolds”, Moscow University Mathematics Bulletin, 70:5 (2015), 213–215  mathnet  crossref  mathscinet  isi
    6. M. B. Banaru, “The Axiom of Sasakian Hypersurfaces and Six-Dimensional Hermitian Submanifolds of the Octonion Algebra”, Math. Notes, 99:1 (2016), 155–159  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Ahmad Abu-Saleem, Mihail B. Banaru, Galina A. Banaru, “A note on $2$-hypersurfaces of the nearly Kählerian six-sphere”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 3, 107–114  mathnet
    8. M. B. Banaru, “On almost contact metric hypersurfaces with type number $1$ or $0$ in $6$-dimensional Hermitian submanifolds of the Cayley algebra”, Siberian Math. J., 58:4 (2017), 559–563  mathnet  crossref  crossref  isi  elib  elib
    9. M. B. Banaru, “O shestimernoi sfere s priblizhenno kelerovoi strukturoi”, Geometriya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 146, VINITI RAN, M., 2018, 3–16  mathnet  mathscinet
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