Totally real submanifold
= Totally real submanifold
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In the maximal-dimension convention, a totally real submanifold of $(M,J)$ has half the real dimension of $M$ and $T_pL\cap J(T_pL)=0$. Every <Lagrangian submanifold> is totally real for a <compatible almost complex structure>, but the converse fails in complex dimension at least two.