Abstract:

For a Lagrangian submanifold of the nearly Kaehler ${\Bbb S}^3\times {\Bbb S}^3$, we provide conditions for a canonically induced almost contact metric structure by a unit vector field, to be $\alpha$-Sasakian, $\beta$-Kenmotsu and cosymplectic. Furthermore, assuming the almost contact metric structure to be normal, we show the conditions when the contact metric structure is $\frac{\sqrt{3}}{3}$-Sasakian, $\frac{\sqrt{3}}{3}$-Kenmotsu or cosymplectic.

Key words: Nearly Kaehler manifold, Lagrangian submanifold, Almost contact metric structure, $\frac{\sqrt{3}}{3}$-Sasakian structure, $\frac{\sqrt{3}}{3}$-Kenmotsu structure, Cosymplectic structure