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Statements

Subject Item: dbr:Projective_geometry
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Beltrami's_theorem
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Ricci_curvature
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Ernest_Julius_Wilczynski
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Georges_Henri_Halphen
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Gerrit_Bol
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Glossary_of_areas_of_mathematics
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Eduard_Čech
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Nigel_Hitchin
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Differential_invariant
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Pauline_Sperry
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Projective_differential_geometry
rdf:type: dbo:Book
rdfs:label: Projective differential geometry
rdfs: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.
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dbo:wikiPageID: 1242592
dbo:wikiPageRevisionID: 977672165
dbo:wikiPageWikiLink: dbr:Function_(mathematics) dbr:Ernest_Julius_Wilczynski dbr:Schwarzian_derivative dbr:Riemannian_geometry dbr:G._Bol dbr:S._P._Finikov dbr:G._F._Laptev dbr:Projective_connection dbr:J._Kanitani dbr:Differential_geometry dbr:Projective_line dbr:Submanifold dbr:Affine_geometry_of_curves dbr:J._G._Darboux dbc:Differential_geometry dbr:Differential_invariant dbr:Eduard_Čech dbr:Erlangen_program dbr:G._Fubini dbr:Élie_Cartan dbr:Projective_group dbr:A._P._Norden dbr:Osculation dbc:Projective_geometry dbr:E._Bompiani dbr:George_Henri_Halphen dbr:Curve dbr:Mathematics dbr:Diffeomorphism dbr:Method_of_moving_frames dbr:Shiing-Shen_Chern
dbo:wikiPageExternalLink: n4:projectivediffer00wilcuoft n16:projective.pdf
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dbo: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, , 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 , Shiing-Shen Chern, , , and . 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.
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Subject Item: dbr:Raymundo_Favila
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Differential_geometry
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Shiing-Shen_Chern
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: dbr:Su_Buqing
dbo:wikiPageWikiLink: dbr:Projective_differential_geometry

Subject Item: wikipedia-en:Projective_differential_geometry
foaf:primaryTopic: dbr:Projective_differential_geometry