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We show that Lagrangian submanifolds in six-dimensional nearly K\"ahler (nonK\"ahler) manifolds and in twistor spaces $Z\sp{4n+2}$ over quaternionicK\"ahler manifolds $Q\sp{4n}$ are minimal. Moreover, we will prove that anyLagrangian submanifold $L$ in a nearly K\"ahler manifold $M$ splits into aproduct of two Lagrangian submanifolds for which one factor is Lagrangian inthe strict nearly K\"ahler part of $M$ and the second factor is Lagrangian inthe K\"ahler part of $M$. Using this splitting theorem we then describeLagrangian submanifolds in nearly K\"ahler manifolds of dimensions six, eightand ten.

Decomposition and minimality of Lagrangian submanifolds in nearly K\"ahler manifolds