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Mat. Sb., 2002, Volume 193, Number 5, Pages 3–16 (Mi msb648)  

This article is cited in 7 scientific papers (total in 7 papers)

Hermitian geometry of 6-dimensional submanifolds of the Cayley algebra

M. B. Banaru


Abstract: Orientable 6-dimensional submanifolds (of general type) of the Cayley algebra are investigated on which the 3-fold vector cross products in the octave algebra induce a Hermitian structure. It is shown that such submanifolds of the Cayley algebra are minimal, non-compact, and para-Kähler, their holomorphic bisectional curvature is positive and vanishes only at the geodesic points.
It is also proved that cosymplectic hypersurfaces of 6-dimensional Hermitian submanifolds of the octave algebra are ruled. A simple test for the minimality of such surfaces is obtained. It is shown that 6-dimensional submanifolds of the Cayley algebra satisfying the axiom of $g$-cosymplectic hypersurfaces are Kähler manifolds.

DOI: https://doi.org/10.4213/sm648

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English version:
Sbornik: Mathematics, 2002, 193:5, 635–648

Bibliographic databases:

UDC: 513.74
MSC: 53C40, 53C55
Received: 20.10.2000

Citation: M. B. Banaru, “Hermitian geometry of 6-dimensional submanifolds of the Cayley algebra”, Mat. Sb., 193:5 (2002), 3–16; Sb. Math., 193:5 (2002), 635–648

Citation in format AMSBIB
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\by M.~B.~Banaru
\paper Hermitian geometry of 6-dimensional submanifolds of the~Cayley algebra
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\vol 193
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\pages 635--648
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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, “On Sasakian hypersurfaces in 6-dimensional Hermitian submanifolds of the Cayley algebra”, Sb. Math., 194:8 (2003), 1125–1136  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. 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
    3. Banaru M.B., “On Kenmotsu hypersurfaces in a six-dimensional Hermitian submanifold of Cayley algebra”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, 2004, 33–40  crossref  mathscinet  zmath  adsnasa  isi
    4. 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
    5. 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
    6. 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
    7. 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
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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