Kähler manifold
A Kähler manifold is a special type of complex manifold that has a compatible symplectic structure. This means it has a complex structure that allows for the definition of a metric, which is a way to measure distances and angles. The metric is also compatible with a symplectic form, a mathematical object that encodes information about the geometry of the manifold.
Kähler manifolds are important in various fields of mathematics and theoretical physics, particularly in the study of complex geometry and string theory. They are named after the mathematician Ernst Kähler, who contributed significantly to the understanding of these structures. Examples of Kähler manifolds include complex projective spaces and certain types of algebraic varieties.