Surfaces of the nearly Kähler S³ × S³ preserved by the almost product structure

Abstract

The product manifold (Formula presented.) 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 (Formula presented.) which are P-invariant.