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This subtopic studies complex manifolds, emphasizing complex structures, holomorphic coordinates, and the geometry of smooth complex spaces.
32M05 studies complex lie groups, group actions on complex spaces in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.
Used in differential geometry, complex analysis, and moduli theory.
32M10 studies homogeneous complex manifolds in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.
Used in differential geometry, complex analysis, and moduli theory.
32M12 studies almost homogeneous manifolds and spaces in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.
Used in differential geometry, complex analysis, and moduli theory.
32M15 studies hermitian symmetric spaces, bounded symmetric domains, jordan algebras in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.
Used in differential geometry, complex analysis, and moduli theory.
32M17 studies automorphism groups of $\mathbb{c}^n$ and affine manifolds in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.
Used in differential geometry, complex analysis, and moduli theory.
32M25 studies complex vector fields, holomorphic foliations, related topics in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.
Used in differential geometry, complex analysis, and moduli theory.