In this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection. We next consider Lie groupoids of fibre morphisms of a fibre bundle, and the connections on such groupoids together with their...Lasīt vairāk
The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such areas as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with &nb...Lasīt vairāk
The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional...Lasīt vairāk
The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifold...Lasīt vairāk
