affine differential geometry
E1017916
Affine differential geometry is a branch of differential geometry that studies geometric properties of submanifolds and spaces invariant under volume-preserving affine transformations.
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
branch of differential geometry
ⓘ
mathematical discipline ⓘ |
| appliesTo |
convex hypersurfaces
ⓘ
improper affine spheres ⓘ proper affine spheres ⓘ |
| characterizedBy |
centroaffine structure
ⓘ
equiaffine structure ⓘ |
| developedFrom |
affine geometry
ⓘ
classical differential geometry ⓘ |
| fieldOfStudy |
affine geometry
ⓘ
differential geometry NERFINISHED ⓘ |
| focusesOn |
Blaschke metric
NERFINISHED
ⓘ
Pick invariant ⓘ affine fundamental forms ⓘ affine normal vector fields ⓘ invariants of affine connections ⓘ properties invariant under affine transformations ⓘ properties invariant under volume-preserving affine transformations ⓘ |
| hasApplicationIn |
Kähler geometry
NERFINISHED
ⓘ
information geometry ⓘ mirror symmetry ⓘ the study of convex bodies ⓘ the theory of Monge–Ampère equations ⓘ |
| hasHistoricalFigure |
Katsumi Nomizu
NERFINISHED
ⓘ
Shiing-Shen Chern NERFINISHED ⓘ Udo Simon NERFINISHED ⓘ Wilhelm Blaschke NERFINISHED ⓘ |
| hasInvariantGroup | special affine group NERFINISHED ⓘ |
| hasTypicalObject |
elliptic affine sphere
ⓘ
hyperbolic affine sphere ⓘ parabolic affine sphere ⓘ |
| relatedTo |
Riemannian geometry
NERFINISHED
ⓘ
convex geometry ⓘ projective differential geometry ⓘ symplectic geometry ⓘ |
| studies |
affine completeness of hypersurfaces
ⓘ
affine geodesics ⓘ affine hypersurfaces ⓘ affine spheres ⓘ centroaffine hypersurfaces ⓘ equiaffine hypersurfaces ⓘ geometric properties of manifolds ⓘ geometric properties of submanifolds ⓘ |
| usesConcept |
affine connection
ⓘ
affine curvature ⓘ affine mean curvature ⓘ affine normal ⓘ affine shape operator ⓘ torsion-free connection ⓘ volume form ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.