A Survey on Lagrangian Submanifolds of Nearly Kaehler Six-Sphere

We first review the nearly Kaehler structure on the six-dimensional unit sphere \(S^6\) and its Lagrangian (totally real) submanifolds. Then we present a survey of results on Lagrangian submanifolds M of the nearly Kähler \(S^6\) in terms of a canonically induced almost contact metric structure, Chen’s equality, normal connection, normal curvature operator, Ricci tensor and conformal flatness. In particular, conditions for M to be Sasakian and totally geodesic unit three-sphere are presented.