Geodesic
Hermitian geometry of 6-dimensional submanifolds of the~Cayley algebra
Sbornik. Mathematics, Tome 193 (2002) no. 5, pp. 635-648

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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. 
@article{SM_2002_193_5_a0,
     author = {M. B. Banaru},
     title = {Hermitian geometry of 6-dimensional submanifolds of {the~Cayley} algebra},
     journal = {Sbornik. Mathematics},
     pages = {635--648},
     publisher = {mathdoc},
     volume = {193},
     number = {5},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_5_a0/}
}
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M. B. Banaru. Hermitian geometry of 6-dimensional submanifolds of the~Cayley algebra. Sbornik. Mathematics, Tome 193 (2002) no. 5, pp. 635-648. http://geodesic.mathdoc.fr/item/SM_2002_193_5_a0/