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Variations, Geometry and Physics
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Editors: Olga Krupkova and David Saunders (Faculty of Science, Palacky Univ., Czech Republic)
Book Description:
This book is a collection of survey articles in a broad field of the geometrical theory of the calculus of variations and its applications in analysis, geometry and physics. It is a commemorative volume to celebrate the sixty-fifth birthday of Professor Demeter Krupka, one of the founders of modern geometric variational theory, and a major contributor to this topic and its applications over the past thirty-five years. All the authors invited to contribute to this volume have established high reputations in their field. The book will exclusively provide a variety of important results, techniques and applications that are usually available only by consulting original papers in many different journals. It will be of interest to researchers in variational calculus, mathematical physics and the other related areas of differential equations, natural operators and geometric structures. Also, it will become an important source of current research for doctoral students and postdoctorals in these fields.

Table of Contents:

Part 1: Variational Principles on Jet Bundles; pp. 1-2
Chapter 1. Lepage forms in Variational Theories: From Lepage's Idea to the Variational Sequence; pp. 3-26
(J. Musilová and M. Lenc)

Chapter 2. Lepage forms in the Calculus of Variations; pp. 27-55
(O. Krupková)

Chapter 3. On a Generalization of the Poincaré-Cartan Form in Higher-Order Field Theory; pp. 57-76
(D. R. Grigore)

Chapter 4. Krupka's Fundamental Lepage Equivalent and the Excess Function of Wilkins; pp. 77-84
(D. J. Saunders)

Chapter 5. Lepage Congruences in Discrete Mechanics; pp. 85-97
(A. Fernández and P. L. García)

Chapter 6. Finite Order Variational Sequences: A short review; pp. 99-115
(R. Vitolo)

Chapter 7. Concatenating Variational Principles and the Kinetic
Stress-Energy-Momentum Tensor; pp. 117-128
(M. Castrillón López, M. J. Gotay and J. E. Marsden)

Chapter 8. A Geometric Hamilton-Jacobi Theory for Classical Field Theories; pp. 129-140
(M. de Léon, J. C. Marrero and D. Martín Diego)

Chapter 9. Part II: Natural Bundles and Differential Invariants Natural Lagrangian Structures; pp. 143-166
(J. Janyška)

Chapter 10. Connections on Higher Order Frame Bundles and Their Gauge; pp. 167-188
Analogies (I. Kolář)

Chapter 11. Natural Lifts in Riemannian geometry; pp. 189-207
(O. Kowalski and M. Sekizawa)

Chapter 12. Invariant Variational Problems and Invariant Flows Via
Moving Frames; pp. 209-235
(P. J. Olver)

Chapter 13. Differential Invariants of the Motion Group Actions; pp. 237-251
(B. Kruglikov and V. Lychagin)

Part III: Differential Equations and Geometrical Structures
Chapter 14. Remarks on the History of the Notion of Lie Differentiation; pp. 255-259
(A. Trautman)

Chapter 15. Second-order Differential Equation Fields with Symmetry; pp. 261-275
(M. Crampin and T. Mestdag)

Chapter 16. Dimensional Reduction of Curvature-dependent Central Potentials on
Spaces of Constant Curvature; pp. 277-291
(J. F. Cariñena, M. F. Ranada and M. Santander)

Chapter 17. Direct Geometrical Method in Finsler Geometry; pp. 293-314
(L. Tamássy)

Chapter 18. Linear Connections Along the Tangent Bundle Projection; pp. 315-340
(W. Sarlet)

Chapter 19. On the Inverse Problem for Autoparallels; pp. 341-351
(G. E. Prince)

Part IV: Appendix
Demeter Krupka: List of publications; pp. 355-362


   Binding: Hardcover
   Pub. Date: 2009
   Pages: 370 pp.
   ISBN: 978-1-60456-920-9
   Status: AV
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
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