Even for the slightest bows, the neck usually does not bend. The entire torso leans forward, with the neck straight. For standing bows, the hands should remain lightly touching the sides of the legs, without moving them, for men. Women sometimes slide their hands inward and downward in formal situations, but this is rarely seen in Karate dojo. With seated bows, hands should slide directly forward to in front of the knees.
Women sometimes bring their hands closer together, as with the formal standing bow.
As far as the position of the eyes goes, there seem to be different opinions on the subject. Some think that it is rude to look an instructor in the eyes when bowing. Some say that you should keep looking into your partner's eyes as you bow. Lowering the eyes is a sign of modesty, and is used in formal bowing in Japan often. But showing gratitude for receiving correction from an instructor is not necessarily worthy of such a deep, downward-looking bow.