Homogenization of integral functionals is studied under the constraint thatadmissible maps have to take their values into a given smooth manifold. Thenotion of tangential homogenization is defined by analogy with the tangentialquasiconvexity introduced by Dacorogna, Fonseca, Maly and Trivisa \cite{DFMT}.For energies with superlinear or linear growth, a $\Gamma$-convergence resultis established in Sobolev spaces, the homogenization problem in the space offunctions of bounded variation being the object of \cite{BM}.
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