Is this a trait common to Azoychka, or should I be worried?

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In my experience growing it it isn't a problem.

But then you ask why that one and not the others?

Not all varieties are the same when it comes to reacting to the environment and curled leaves can occur if it's too hot, too cool, too wet or too dry or if a plant has a heavy burden of tomatoes.

So I would expect to see differences in varieties when considering those varaibles.

If the leaves curl over into a tube then look for aphids. And if symptoms get more serious then let us know about that.

Carolyn