In differential geometry, geometrical objects are examined primarily using differential calculus. Differential calculus allows us, for example, to examine the curvature of a figure. You may recall that in high school we used differential calculus to study the increase or decrease of a function. Differential geometry covers a very wide range of topics, but in our laboratory, we are particularly interested in differential geometry related to integrable systems, geometric variational problems, and refined differential geometry.

When looking at a circle or a sphere with a constant radius, there are probably not many people who would consider it not beautiful. Then, why do we think such a shape is beautiful? One answer that is likely to be agreed upon by many people is that a circle or a sphere with a constant radius is curved in the same way no matter where you look at it. In the field of differential geometry, we can clearly describe and investigate mathematically how a circle or sphere is curved in the same way as shown above.