Thank you all for your answers!

The conclusion is pretty clear: the differential operators will *not* be 
added to the global namespace at start, even less be added silently when a 
pseudo-Riemannian manifold is constructed. The only way to get them will be 
an explicit demand from the user, in the form of a Python import:
from sage.manifolds.operators import *
or even more explicitly:
from sage.manifolds.operators import grad, div, curl, laplacian
It seems pretty safe to keep the standard notations here (i.e. "grad" 
instead of "gradient" and "div" instead of "divergence"), because the 
context of the import is clearly that of differential geometry. If for some 
reason, the name "div" was already used, it remains possible to do 
from sage.manifolds.operators import div as divergence.


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