differential geometric object
C3506
concept
A differential geometric object is a mathematical entity, such as a manifold, tensor, or connection, defined on smooth spaces and characterized by properties that are invariant under smooth coordinate transformations.
All labels observed (28)
| Label | Occurrences |
|---|---|
| differential geometry concept | 3 |
| differential form | 2 |
| geometric connection | 2 |
| identity in differential geometry | 2 |
| map between manifolds | 2 |
| smooth manifold | 2 |
| structure in symplectic geometry | 2 |
| symplectic form | 2 |
| Clifford algebra formalism | 1 |
| Kähler manifold | 1 |
| Lie algebra-valued 1-form | 1 |
| affine connection | 1 |
| closed 2-form | 1 |
| connection in differential geometry | 1 |
| differential geometric object canonical | 1 |
| differential geometric operator | 1 |
| differential geometric quantity | 1 |
| differential geometric structure | 1 |
| differential-geometric structure | 1 |
| generalization of Riemannian connection | 1 |
| generalization of affine connection | 1 |
| left-invariant Riemannian geometry | 1 |
| object in differential geometry | 1 |
| real 3-dimensional manifold | 1 |
| smooth manifold with additional structure | 1 |
| surface diffeomorphism | 1 |
| symplectic manifold | 1 |
| tool in differential topology | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: differential geometric object
Generated description
A differential geometric object is a mathematical entity, such as a manifold, tensor, or connection, defined on smooth spaces and characterized by properties that are invariant under smooth coordinate transformations.
Instances (31)
| Instance | Via concept surface |
|---|---|
|
Cartan connection
linked to:
Cartan connections
|
connection in differential geometry |
| Kähler form | differential form |
| Calabi–Yau manifold | Kähler manifold |
| Lie group | smooth manifold |
| Weingarten map | differential geometric operator |
| spacetime algebra | Clifford algebra formalism |
| Levi-Civita connection | affine connection |
| Kähler manifold | symplectic manifold |
| Dehn twist | surface diffeomorphism |
| Gaussian curvature | differential geometry concept |
| Gauss map | differential geometry concept |
|
Riemannian manifold
linked to:
Riemannian manifolds
|
— |
| Lefschetz fibration | structure in symplectic geometry |
|
SU(2)
linked to:
rotation group SU(2)
|
real 3-dimensional manifold |
| Weyl geometry | differential geometric structure |
| Pfaffian form | object in differential geometry |
| Whitney stratification | tool in differential topology |
| Maurer–Cartan form | Lie algebra-valued 1-form |
| Fubini–Study form | symplectic form |
| Poisson bracket | structure in symplectic geometry |
| Ricci scalar | differential geometric quantity |
| Cartan magic formula | identity in differential geometry |
|
Bochner identity
linked to:
Bochner
|
identity in differential geometry |
| shape operator | differential geometry concept |
| Hopf fibration | map between manifolds |
| Jacobi manifold | differential-geometric structure |
|
Chern–Simons form
linked to:
Chern–Simons forms
|
differential form |
| Hitchin connection | geometric connection |
| Nil geometry | left-invariant Riemannian geometry |
| 4-sphere S^4 | smooth manifold |
| non-Abelian Berry connection | geometric connection |