French translation for "cotangent bundle"

fibré cotangent

Example Sentences:

	1.	Examples of this M in physics include: In classical mechanics, in the Hamiltonian formulation, M is the one-dimensional manifold R, representing time and the target space is the cotangent bundle of space of generalized positions. Avant tout donnons quelques exemples : En mécanique classique, dans le formalisme d'Hamilton, M
	2.	The principal symbol of P, denoted σP, is the function on the cotangent bundle T∗X defined in these local coordinates by σ P ( x , ξ ) = ∑ | α | = k P α ( x ) ξ α {\displaystyle \sigma _{P}(x,\xi )=\sum _{|\alpha |=k}P^{\alpha }(x)\xi _{\alpha }} where the ξi are the fiber coordinates on the cotangent bundle induced by the coordinate differentials dxi. Le symbole principal de P, noté σP, est la fonction sur le fibré cotangent T∗X défini dans un système de coordonnées local ξi par σ P ( x , ξ ) = ∑ | α | = k P α ( x ) ξ α
	3.	The principal symbol of P, denoted σP, is the function on the cotangent bundle T∗X defined in these local coordinates by σ P ( x , ξ ) = ∑ | α | = k P α ( x ) ξ α {\displaystyle \sigma _{P}(x,\xi )=\sum _{|\alpha |=k}P^{\alpha }(x)\xi _{\alpha }} where the ξi are the fiber coordinates on the cotangent bundle induced by the coordinate differentials dxi. Le symbole principal de P, noté σP, est la fonction sur le fibré cotangent T∗X défini dans un système de coordonnées local ξi par σ P ( x , ξ ) = ∑ | α | = k P α ( x ) ξ α
	4.	If we take E to be the sum of the even exterior powers of the cotangent bundle, and F to be the sum of the odd powers, define D = d + d*, considered as a map from E to F. Then the topological index of D is the Euler characteristic of the Hodge cohomology of M, and the analytical index is the Euler class of the manifold. Prenant pour E la somme des puissances extérieures paires du fibré cotangent, et pour F la somme des puissances impaires, posons D =d + d*, considéré comme une application de E vers F. Alors l'indice topologique de D est la caractéristique d'Euler de M, et l'indice analytique est la somme alternée des dimensions des groupes de cohomologie de de Rham.

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