We prove that a compact Riemann surface can be realized as a pseudo-holomorphic curve of (R4, J), for some almost complex structure J if and only if it is an elliptic curve. Furthermore, we show that any (almost) complex 2n-torus can be holomorphically embedded in (R4n, J) for a suitable almost complex structure J. This allows us to embed any compact Riemann surface in some almost complex Euclidean space and to show many explicit examples of almost complex structures in R2n, which cannot be tamed by any symplectic form.



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