Properties of the Nearly Kähler ${𝕊}^3\times {𝕊}^3$

Marilena Moruz, Luc Vrancken

Abstract: We show how the metric, the almost complex structure and the almost product structure of the homogeneous nearly Kähler ${𝕊}^3\times {𝕊}^3$ can be recovered from a submersion $\pi :{𝕊}^3\times {𝕊}^3\times {𝕊}^3\to {𝕊}^3\times {𝕊}^3$. On ${𝕊}^3\times {𝕊}^3\times {𝕊}^3$ we have the maps obtained either by changing two coordinates, or by cyclic permutations.

Keywords: nearly Kähler manifolds; Riemannian submersion

Classification (MSC2000): 53B35

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