On Almost Complex Structures on 6-dimensional Products of Spheres
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 116-135
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In this article, almost complex structures on the sphere $S^6$ and on the products of spheres $S^1\times S^5$, $S^2\times S^4$, and $S^3\times S^3$ which naturally arise at their embeddings in the algebra of Cayley numbers are considered. It is shown that all of them are nonintegrable. Expressions of the fundamental form $\omega$ and the Nijenhuis tensor for each case are obtained. It is also shown that the form $d\omega$ is nondegenerate. New special almost complex structures on products of spheres are constructed.
Keywords:
6-manifolds, almost complex structures, Cayley numbers, vector cross product.
@article{UZKU_2009_151_4_a9,
author = {N. K. Smolentsev},
title = {On {Almost} {Complex} {Structures} on 6-dimensional {Products} of {Spheres}},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {116--135},
publisher = {mathdoc},
volume = {151},
number = {4},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a9/}
}
TY - JOUR AU - N. K. Smolentsev TI - On Almost Complex Structures on 6-dimensional Products of Spheres JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2009 SP - 116 EP - 135 VL - 151 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a9/ LA - ru ID - UZKU_2009_151_4_a9 ER -
%0 Journal Article %A N. K. Smolentsev %T On Almost Complex Structures on 6-dimensional Products of Spheres %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2009 %P 116-135 %V 151 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a9/ %G ru %F UZKU_2009_151_4_a9
N. K. Smolentsev. On Almost Complex Structures on 6-dimensional Products of Spheres. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 116-135. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a9/