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In this paper, we investigate Lagrangian submanifolds in the nearly Kaehler$S^3 \times S^3$. We construct a new example which is a at Lagrangian torus. Wegive a complete classification of all the Lagrangian immersions of spaces ofconstant sectional curvature in the nearly Kaehler $S^3\times S^3$.

Lagrangian submanifolds in the nearly kaehler $s^3 \times s^3$