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- Projective_differential_geometry abstract "In mathematics, projective differential geometry is the study of differential geometry, from the point of view of properties of mathematical objects. such as functions, diffeomorphisms, and submanifolds, that are invariant under transformations of the projective group. This is a mixture of the approaches from Riemannian geometry of studying invariances, and of the Erlangen program of characterizing geometries according to their group symmetries. The area was much studied by mathematicians from around 1890 for a generation (by J. G. Darboux, George Henri Halphen, Ernest Julius Wilczynski, E. Bompiani, G. Fubini, Eduard Čech, amongst others), without a comprehensive theory of differential invariants emerging. Élie Cartan formulated the idea of a general projective connection, as part of his method of moving frames; abstractly speaking, this is the level of generality at which the Erlangen program can be reconciled with differential geometry, while it also develops the oldest part of the theory (for the projective line), namely the Schwarzian derivative, the simplest projective differential invariant.Further work from the 1930s onwards was carried out by J. Kanitani, Shiing-Shen Chern, A. P. Norden, G. Bol, S. P. Finikov and G. F. Laptev. Even the basic results on osculation of curves, a manifestly projective-invariant topic, lack any comprehensive theory. The ideas of projective differential geometry recur in mathematics and its applications, but the formulations given are still rooted in the language of the early twentieth century.".
- Projective_differential_geometry wikiPageExternalLink projectivediffer00wilcuoft.
- Projective_differential_geometry wikiPageExternalLink projective.pdf.
- Projective_differential_geometry wikiPageID "1242592".
- Projective_differential_geometry wikiPageRevisionID "570857575".
- Projective_differential_geometry hasPhotoCollection Projective_differential_geometry.
- Projective_differential_geometry subject Category:Differential_geometry.
- Projective_differential_geometry subject Category:Projective_geometry.
- Projective_differential_geometry comment "In mathematics, projective differential geometry is the study of differential geometry, from the point of view of properties of mathematical objects. such as functions, diffeomorphisms, and submanifolds, that are invariant under transformations of the projective group. This is a mixture of the approaches from Riemannian geometry of studying invariances, and of the Erlangen program of characterizing geometries according to their group symmetries.".
- Projective_differential_geometry label "Projective differential geometry".
- Projective_differential_geometry sameAs m.04lk62.
- Projective_differential_geometry sameAs Q7249466.
- Projective_differential_geometry sameAs Q7249466.
- Projective_differential_geometry wasDerivedFrom Projective_differential_geometry?oldid=570857575.
- Projective_differential_geometry isPrimaryTopicOf Projective_differential_geometry.