| 32Q05 | Negative curvature manifolds |
| 32Q10 | Positive curvature manifolds |
| 32Q15 | Kähler manifolds |
| 32Q20 | Kähler-Einstein manifolds [See also 53Cxx] |
| 32Q25 | Calabi-Yau theory |
| 32Q28 | Stein manifolds |
| 32Q30 | Uniformization |
| 32Q35 | Complex manifolds as subdomains of Euclidean space |
| 32Q40 | Embedding theorems |
| 32Q45 | Hyperbolic and Kobayashi hyperbolic manifolds |
| 32Q55 | Topological aspects of complex manifolds |
| 32Q57 | Classification theorems |
| 32Q60 | Almost complex manifolds |
| 32Q65 | Pseudoholomorphic curves |
| 32Q99 | None of the above, but in this section |