**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 Geometry: Preliminaries, 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 ...

### Famous quotes containing the words geometry and/or differential:

“I am present at the sowing of the seed of the world. With a *geometry* of sunbeams, the soul lays the foundations of nature.”

—Ralph Waldo Emerson (1803–1882)

“But how is one to make a scientist understand that there is something unalterably deranged about *differential* calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”

—Antonin Artaud (1896–1948)