Pseudoholomorphic curves

Pseudoholomorphic curves are mathematical objects that generalize the notion of smooth, curved surfaces within a space, but with a special property: they preserve a structure that combines complex and real geometries. Specifically, these curves are maps from a two-dimensional surface into a higher-dimensional space, respecting a particular “almost complex” structure that aligns with complex number behaviors. They are important in symplectic geometry and string theory because they help understand the shape and properties of complex spaces, providing insights into both mathematical and physical phenomena.