Geodesic
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. 
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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/

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