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

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

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English version:
Siberian Mathematical Journal, 2003, 44:5, 765–773

Bibliographic databases:

UDC: 513.82
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
\Bibitem{Ban03} \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. \yr 2003 \vol 44 \issue 5 \pages 981--991 \mathnet{http://mi.mathnet.ru/smj1246} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2019552} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000186135400003} 

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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
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
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
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
5. M. B. Banaru, “The axiom of cosymplectic surfaces and $W_4$-manifolds”, Moscow University Mathematics Bulletin, 70:5 (2015), 213–215
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
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
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
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
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