[…]projectivedifferential geometries of the American and Italian schools do not seem to have attracted physicists.
1962, I. M. James,The Mathematical Works of J. H. C. Whitehead, Volume 1:Differential Geometry,page 189,
The general theory of manifolds of class 2 is a sub-class ofdifferential geometries, which contain the theory of affine connections, curvature and osculating sub-spaces.
1993, M. A. Akivis, V. V. Goldberg,ProjectiveDifferential Geometry of Submanifolds,page v:
Note that projectivedifferential geometry is a basis for Euclidean and non-Euclideandifferential geometries since metric properties of submanifolds of Euclidean and non-Euclidean spaces should only be added to their projective properties.
2012, Heinrich W. Guggenheimer,Differential Geometry,page145:
In this sense, is the natural hypothesis of differentiability in the particular question ofdifferential geometry.
