For a Lagrangian submanifold M of S 6 with nearly Kaehler structure, we provide conditions for a canonically induced almost contact metric structure on M by a unit vector field, to be Sasakian. Assuming M contact metric, we show that it is Sasakian if and only if the second fundamental form annihilates the Reeb vector field ξ, furthermore, if the Sasakian submanifold M is parallel along ξ, then it is the totally geodesic 3-sphere. We conclude with a condition that reduces the normal canonical almost contact metric structure on M to Sasakian or cosymplectic structure.
Sharma, Ramesh; Deshmukh, Sharief; and Al-Solamy, Falleh, "Almost Contact Lagrangian Submanifolds of Nearly Kaehler 6-Sphere" (2014). Mathematics Faculty Publications. 3.
Almost contact Lagrangian submanifolds of nearly Kaehler 6-sphere (with S. Deshmukh and F. Al-Solamy), Results in Mathematics 65 (2014), 143-153.