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You can get nabla via nabla = E.metric().connection(), where E is the Euclidean space; then you apply it to the vector v by nabla(v), not by means of the tensor product. Here is a full example:
sage: E.<x,y,z> = EuclideanSpace()
sage: v = E.vector_field(-y, x^2, 1+x*y)
sage: nabla = E.metric().connection()
sage: nabla
Levi-Civita connection nabla_g associated with the Riemannian metric g on the Euclidean space E^3
sage: t = nabla(v)
sage: t
Tensor field of type (1,1) on the Euclidean space E^3
sage: t[:]
[ 0 -1 0]
[2*x 0 0]
[ y x 0]