141:, 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.
98:; 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
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Projective
Differential Geometry Old and New From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups
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The area was much studied by mathematicians from around 1890 for a generation (by
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of characterizing geometries according to their group symmetries.
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Projective differential geometry of curves and ruled surfaces
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Further work from the 1930s onwards was carried out by
179:. Cambridge University Press. p. vii (preface).
82:, amongst others), without a comprehensive theory of
106:, the simplest projective differential invariant.
43:, that are invariant under transformations of the
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47:. This is a mixture of the approaches from
215:Notes on Projective Differential Geometry
170:V. Ovsienko and S. Tabachnikov (2004).
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51:of studying invariances, and of the
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90:formulated the idea of a general
25:projective differential geometry
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204:(Leipzig: B.G. Teubner,1906)
133:. Even the basic results on
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198:Ernest Julius Wilczynski
151:Affine geometry of curves
68:Ernest Julius Wilczynski
96:method of moving frames
84:differential invariants
231:Differential geometry
104:Schwarzian derivative
92:projective connection
29:differential geometry
64:George Henri Halphen
236:Projective geometry
217:by Michael Eastwood
49:Riemannian geometry
115:Shiing-Shen Chern
94:, as part of his
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53:Erlangen program
45:projective group
27:is the study of
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209:Further reading
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100:projective line
37:diffeomorphisms
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131:G. F. Laptev
119:A. P. Norden
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41:submanifolds
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111:J. Kanitani
88:Élie Cartan
80:Eduard Čech
72:E. Bompiani
21:mathematics
225:Categories
157:References
135:osculation
86:emerging.
76:G. Fubini
33:functions
145:See also
16:Geometry
183:
139:curves
123:G. Bol
39:, and
177:(PDF)
181:ISBN
129:and
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19:In
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