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h-Principle phi-free embeddings in calibrated manifolds

In this paper, we prove that the h-principle holds for phi-free embeddings for coassociative, Cay ley and quaternionic calibrations. As a result, we show that for coassocative calibration *partial derivative, an orientable smooth closed 4-manifold N-4 can be embedded into any G(2)-manifold M-7 as *partial derivative-free if the Euler characteristic of N, chi(N) and the signature of N, tau(N) are equal to zero.