A Kähler metric is a special type of Riemannian metric used in differential geometry, particularly in the study of complex manifolds. It combines a symplectic structure with a compatible complex structure, allowing for a rich interplay between geometry and complex analysis. This metric is defined by a Kähler potential, which is a real-valued function whose second derivatives yield the metric. Kähler metrics are significant in various fields, including string theory and algebraic geometry. They help in understanding the geometric properties of complex spaces and play a crucial role in the study of Calabi-Yau manifolds, which are important in theoretical physics and mathematics.