Complex geometry is a branch of mathematics that studies geometric structures using the principles of complex numbers. It combines ideas from both geometry and complex analysis, focusing on shapes and spaces that can be described with complex coordinates. This field often explores properties of complex manifolds, which are higher-dimensional spaces that locally resemble complex number spaces. One important aspect of complex geometry is the study of Kähler manifolds, which have special symmetries and are significant in both mathematics and theoretical physics. Researchers also investigate Riemann surfaces, which are one-dimensional complex manifolds, to understand their unique properties and applications in various scientific fields.