Higher order absolute differentiation with respect to generalized connections
Ivan Kolář (1984)
Banach Center Publications
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Ivan Kolář (1984)
Banach Center Publications
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Petr Vašík (2011)
Banach Center Publications
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We recall several different definitions of semiholonomic jet prolongations of a fibered manifold and use them to derive some interesting properties of prolongation of a first order connection to a third order semiholonomic connection.
Josef Janyška (2011)
Annales Polonici Mathematici
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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.
Alena Vanžurová (1983)
Časopis pro pěstování matematiky
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Ivan Kolář (1969)
Commentationes Mathematicae Universitatis Carolinae
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Vladimír Lešovský (1982)
Archivum Mathematicum
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Ivan Kolář (1981)
Archivum Mathematicum
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Miroslav Doupovec, Włodzimierz M. Mikulski (2011)
Annales Polonici Mathematici
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We describe all bundle functors G admitting natural operators transforming rth order holonomic connections on a fibered manifold Y → M into rth order holonomic connections on GY → M. For second order holonomic connections we classify all such natural operators.
Miroslav Doupovec, Włodzimierz M. Mikulski (2011)
Annales Polonici Mathematici
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We introduce exchange natural equivalences of iterated nonholonomic, holonomic and semiholonomic jet functors, depending on a classical linear connection on the base manifold. We also classify some natural transformations of this type. As an application we introduce prolongation of higher order connections to jet bundles.