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
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.
PDF file (269 kB)
Sbornik: Mathematics, 2002, 193:5, 635–648
MSC: 53C40, 53C55
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
\paper Hermitian geometry of 6-dimensional submanifolds of the~Cayley algebra
\jour Mat. Sb.
\jour Sb. Math.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
M. B. Banaru, “On Sasakian hypersurfaces in 6-dimensional Hermitian
submanifolds of the Cayley algebra”, Sb. Math., 194:8 (2003), 1125–1136
M. B. Banaru, “On the Kenmotsu hypersurfaces of special Hermitian manifolds”, Siberian Math. J., 45:1 (2004), 7–10
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
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
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
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
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
|Number of views:|