Affine Differential Geometry

Affine differential geometry, is a type of differential geometry in which the differential invariants are invariant under volume-preserving affine transformations. The name affine differential geometry follows from Klein's Erlangen program. The basic difference between affine and Riemannian differential geometry is that in the affine case we introduce volume forms over a manifold instead of metrics.

Read more about Affine Differential GeometryPreliminaries, The First Induced Volume Form, The Second Induced Volume Form, Two Natural Conditions, The Conclusion, The Affine Normal Line

Other articles related to "affine differential geometry, affine":

Affine Differential Geometry - The Affine Normal Line - Surfaces in 3-space
... A similar analogue exists for finding the affine normal line at elliptic points of smooth surfaces in 3-space ... locus as one tends to the original surface point is the affine normal line, i.e ... the line containing the affine normal vector ...

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