The phrase "in curvatures" refers to something that is bent or curved, but if we were to look for antonyms to this phrase, we would be talking about things that are straight or rigid. Other words that could be used as antonyms for "in curvatures" include "linear," "straightforward," "direct," "unbending," "unwavering," and "unyielding." When thinking about antonyms for phrases, it is important to focus on the opposite meaning or idea. In the case of "in curvatures," straightness and rigidity would be the opposites, rather than other alternative possibilities such as sharpness, softness, or color.