tailieunhanh - NATURAL OPERATIONS IN DIFFERENTIAL GEOMETRYIvan Kol´ˇ ar Peter W. Michor Jan Slov´k aMailing

NATURAL OPERATIONS IN DIFFERENTIAL GEOMETRY Ivan Kol´ˇ ar Peter W. Michor Jan Slov´k a Mailing address: Peter W. Michor, Institut f¨r Mathematik der Universit¨t Wien, u a Strudlhofgasse 4, A-1090 Wien, Austria. Ivan Kol´ˇ, Jan Slov´k, ar a Department of Algebra and Geometry Faculty of Science, Masaryk University Jan´ˇkovo n´m 2a, CS-662 95 Brno, Czechoslovakia ac a Electronic edition. Originally published by Springer-Verlag, Berlin Heidelberg 1993, ISBN 3-540-56235-4, ISBN 0-387-56235-4. Typeset by AMS-TEX .v TABLE OF CONTENTS PREFACE . . . . . . . . . . . . . . . . . . . . . . . . CHAPTER I. MANIFOLDS AND LIE. | NATURAL OPERATIONS IN DIFFERENTIAL GEOMETRY Ivan Kolar Peter W. Michor Jan Slovak Mailing address Peter W. Michor Institut fur Mathematik der Universitat Wien Strudlhofgasse 4 A-1090 Wien Austria. Ivan Kolar Jan Slovak Department of Algebra and Geometry Faculty of Science Masaryk University Janackovo nám 2a CS-662 95 Brno Czechoslovakia Electronic edition. Originally published by Springer-Verlag Berlin Heidelberg 1993 ISBN 3-540-56235-4 ISBN 0-387-56235-4. Typeset by AmS-TeX v TABLE OF CONTENTS PREFACE . 1 CHAPTER I. MANIFOLDS AND LIE GROUPS .4 1. Differentiable manifolds .4 2. Submersions and 3. Vector fields and 4. Lie 5. Lie subgroups and homogeneous spaces .41 CHAPTER II. DIFFERENTIAL 6. Vector 7. Differential 8. Derivations on the algebra of differential forms and the Frolicher-Nijenhuis bracket .67 CHAPTER III. BUNDLES AND CONNECTIONS .76 9. General fiber bundles and connections . 76 10. Principal fiber bundles and 11. Principal and induced connections . 99 CHAPTER IV. JETS AND NATURAL 12. 13. Jet groups . 128 14. Natural bundles and operators . 138 15. Prolongations of principal fiber bundles . 149 16. Canonical differential forms . 154 17. Connections and the absolute differentiation . 158 CHAPTER V. FINITE ORDER THEOREMS . 168 18. Bundle functors and natural operators . 169 19. Peetre-like theorems . 176 20. The regularity of bundle 21. Actions of jet 22. The order of bundle functors . 202 23. The order of natural operators . 205 CHAPTER VI. METHODS FOR FINDING NATURAL OPERATORS . 212 24. Polynomial GL V -equivariant maps .213 25. Natural operators on linear connections the exterior differential . . 220 26. The tensor evaluation theorem . 223 27. Generalized invariant 28. The orbit reduction . 233 29. The method of differential equations . 245 Electronic edition of Natural Operations in Differential Geometry Springer-Verlag .

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