Why is a Japanese sword curved?
The design probably got that way through trial and error. A lot about early sword making is lost. In a humid climate like Japan metal can corrode very quickly. As smiths started developing ideas brought from China and Korea, they began to settle on a single edged, curved design. The depth of this curve has changed over time. At one stage the bend was quite pronounced. A curved blade is very good at cutting and Japanese sword styles either were based on, or changed to fit, this design. We need to remember that the Japanese sword developed to meet a very specific set of challenges. Over time, warriors and smiths decided that a curve worked best for them. Unlike in Europe, armor changed very little over the centuries, necessitating fairly few changes in sword design.