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We prove the (first) reduction theorem for general and classical connections, i.e. we prove that any natural operator of a general connection Γ on a fibered manifold and a classical connection Λ on the base manifold can be expressed as a zero order operator of the curvature tensors of Γ and Λ and their appropriate derivatives.
Josef Janyška. "Reduction theorem for general connections." Annales Polonici Mathematici 102.3 (2011): 231-254. <http://eudml.org/doc/280454>.
@article{JosefJanyška2011, abstract = {We prove the (first) reduction theorem for general and classical connections, i.e. we prove that any natural operator of a general connection Γ on a fibered manifold and a classical connection Λ on the base manifold can be expressed as a zero order operator of the curvature tensors of Γ and Λ and their appropriate derivatives.}, author = {Josef Janyška}, journal = {Annales Polonici Mathematici}, keywords = {general connection; classical connection; normal coordinates; natural bundle; natural operator; general covariant derivative; reduction theorem}, language = {eng}, number = {3}, pages = {231-254}, title = {Reduction theorem for general connections}, url = {http://eudml.org/doc/280454}, volume = {102}, year = {2011}, }
TY - JOUR AU - Josef Janyška TI - Reduction theorem for general connections JO - Annales Polonici Mathematici PY - 2011 VL - 102 IS - 3 SP - 231 EP - 254 AB - We prove the (first) reduction theorem for general and classical connections, i.e. we prove that any natural operator of a general connection Γ on a fibered manifold and a classical connection Λ on the base manifold can be expressed as a zero order operator of the curvature tensors of Γ and Λ and their appropriate derivatives. LA - eng KW - general connection; classical connection; normal coordinates; natural bundle; natural operator; general covariant derivative; reduction theorem UR - http://eudml.org/doc/280454 ER -