Global shift operators and the higher order calculus of variations. (English) Zbl 0781.58001
Summary: We prove the existence of global shift operators \(S\) associated with any fiber bundle \(\pi: E\to M\), and we discuss the use of these operators in the higher order calculus of variations. We use a recent formulation of the variational theory which combines shift operators together with another fundamental operator, called the omega operator, to describe the major aspects of the higher order theory: in particular the Euler operator and the various Cartan operators. This approach provides, we believe, a simple and direct treatment of the subject.
MSC:
| 58A15 | Exterior differential systems (Cartan theory) |
| 49S05 | Variational principles of physics |
| 53C05 | Connections (general theory) |
Keywords:
higher order variational theory; Cartan forms; existence of global shift operators; higher order calculus of variations; omega operator; Euler operator; Cartan operators; global shift operatorsReferences:
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