: These are spaces that locally look like complex
: Lie groups are differentiable manifolds that also possess a group structure, meaning their multiplication and inversion operations are smooth. A Complex Lie Group specifically requires these operations to be holomorphic. Complex Geometry and Lie Theory
is a rich intersection of mathematics where the study of complex analytic structures on manifolds meets the theory of continuous symmetries. This field is fundamental to modern pure mathematics and theoretical physics, particularly in string theory and general relativity. Fundamental Concepts : These are spaces that locally look like
: A central class of complex manifolds that possess a specialized metric (a "Kähler metric") allowing for the use of powerful tools like Hodge theory and Lefschetz theorems. Key Intersections and Applications Go to product viewer dialog for this item. This field is fundamental to modern pure mathematics
Lie Groups, Physics, and Geometry: An Introduction for Physicists, Engineers and Chemists
) and are equipped with holomorphic (complex-differentiable) coordinate transitions.