A Kähler metric is a special type of metric used in differential geometry, particularly in the study of complex manifolds. It combines both a Riemannian metric and a symplectic form, allowing for a rich structure that is compatible with complex structures. This means that the geometry can be analyzed using both real and complex methods. In a Kähler manifold, the metric is defined in such a way that it preserves the complex structure and has a closed Kähler form. This property makes Kähler metrics important in various fields, including string theory and algebraic geometry, as they help in understanding the geometric properties of complex spaces.