# Category:Structures on manifolds

Here is a list of articles in the category **Structures on manifolds** of the Computing portal that unifies foundations of mathematics and computations using computers. There are three main types of structures important on manifolds. The foundational geometric structures are piecewise linear, mostly studied in geometric topology, and smooth manifold structures on a given topological manifold, which are the concern of differential topology as far as classification goes. Building on a smooth structure, there are:

- various G-structures, which relate the tangent bundle to some subgroup
*G*of the general linear group - structures defined by holonomy conditions.

These can be related, and (for example for Calabi–Yau manifolds) their existence can be predicted using discrete invariants.

## Pages in category "Structures on manifolds"

The following 52 pages are in this category, out of 52 total.

### (

- (G,X)-manifold
*(computing)*

### *

- Categories of manifolds
*(computing)*

### A

- Affine manifold
*(computing)* - Analytic manifold
*(computing)*

### B

- Banach manifold
*(computing)* - Edmond Bonan
*(biography)*

### C

- Calibrated geometry
*(computing)* - Canonical ring
*(computing)* - Clifford module bundle
*(computing)*

### F

- Foliation
*(computing)* - Fréchet manifold
*(computing)* - Frölicher space
*(computing)* - Fubini–Study metric
*(computing)*

### G

- G-structure on a manifold
*(computing)* - G2 manifold
*(computing)* - G2-structure
*(computing)* - Generalized complex structure
*(computing)* - Gibbons–Hawking space
*(computing)*

### H

- Hauptvermutung
*(computing)* - Hermitian connection
*(computing)* - Hermitian manifold
*(computing)* - Hilbert manifold
*(computing)* - Hilbert–Smith conjecture
*(computing)* - Hodge structure
*(computing)* - Hypercomplex manifold
*(computing)* - Hyperkähler manifold
*(computing)*

### K

- Killing spinor
*(computing)* - Kirby–Siebenmann class
*(computing)* - Kosmann lift
*(computing)*

### L

- Linear complex structure
*(computing)* - Lipschitz continuity
*(computing)*

### M

- Metaplectic structure
*(computing)*

### O

- Open book decomposition
*(computing)*

### P

- Pachner moves
*(computing)* - Piecewise linear manifold
*(computing)*

### Q

- Quaternion-Kähler manifold
*(computing)* - Quaternion-Kähler symmetric space
*(computing)* - Quaternionic manifold
*(computing)*

### R

- Real structure
*(computing)*

### S

- Sasakian manifold
*(computing)* - Simplicial manifold
*(computing)* - Smooth structure
*(computing)* - Solvmanifold
*(computing)* - Spin structure
*(computing)* - Spinor bundle
*(computing)* - Spinor field
*(physics)* - Supermanifold
*(computing)* - Symplectic frame bundle
*(computing)* - Symplectic spinor bundle
*(computing)* - Symplectization
*(computing)*

### T

- Toric manifold
*(computing)* - Triangulation (topology)
*(computing)*