Surfaces of the nearly Kähler S3×S3${\bf \mathbb {S}^3\times \mathbb {S}^3}$ preserved by the almost product structure

Abstract

Abstract The product manifold is one of the only four homogeneous six‐dimensional nearly Kähler manifolds. It also admits a canonical almost product structure P , which is compatible with the almost complex structure (see Bolton et al., Tôhoku Math. J. 67 (2015), 1–17, and Moruz and Vrancken, Publ. Inst. Math. 103 (2018), no. 117, 147–158). In this paper, we investigate and describe the two‐dimensional surfaces of which are P ‐invariant.