Talk:Affine connection

Affine connection independence: new section

← Previous revision Revision as of 02:58, 16 April 2026 Line 23: Line 23:

Cartan 1926 Acta Math. paper title is actually "Les groupes d’holonomie des espaces généralisés". Title in Wikipedia article became "Espaces à connexion affine, projective et conforme". I do not know whether the title or the ref is wrong. [[User:Arnaud Chéritat|Arnaud Chéritat]] ([[User talk:Arnaud Chéritat|talk]]) 21:33, 15 June 2022 (UTC) Cartan 1926 Acta Math. paper title is actually "Les groupes d’holonomie des espaces généralisés". Title in Wikipedia article became "Espaces à connexion affine, projective et conforme". I do not know whether the title or the ref is wrong. [[User:Arnaud Chéritat|Arnaud Chéritat]] ([[User talk:Arnaud Chéritat|talk]]) 21:33, 15 June 2022 (UTC)
== Affine connection independence ==
" It follows from property 1 above that the value of {{math|∇_''X''''Y''}} at a point {{math|''x'' ∈ ''M''}} depends only on the value of {{mvar|X}} at {{mvar|x}} and not on the value of {{mvar|X}} on {{math|''M'' − {''x''}<nowiki/>}}. Can anybody explain why this is true? Given that {{math|f}} has to be smooth, it seems to me like {{math|∇_''X''''Y''}} should depend on the value of {{math|f}} in a neighborhood of {{math|x}} rather than just at {{math|x}}. [[User:ThetaMinusSinTheta|ThetaMinusSinTheta]] ([[User talk:ThetaMinusSinTheta|talk]]) 02:58, 16 April 2026 (UTC)