میدان‌های برداری هارمونیک ۲۰۱۱
Harmonic Vector Fields 2011

1. Cover image

2. Table of Contents

3. Front Matter

4. Copyright

5. Preface

6. Chapter One. Geometry of the Tangent Bundle

7. Chapter Two. Harmonic Vector Fields

2.1. Vector Fields as Isometric Immersions

2.2. The Energy of a Vector Field

2.3. Vector Fields Which Are Harmonic Maps

2.4. The Tension of a Vector Field

2.5. Variations through Vector Fields

2.6. Unit Vector Fields

2.7. The Second Variation of the Energy Function

2.8. Unboundedness of the Energy Functional

2.9. The Dirichlet Problem

2.10. Conformal Change of Metric on the Torus

2.11. Sobolev Spaces of Vector Fields

19. Chapter Three. Harmonicity and Stability

3.1. Hopf Vector Fields on Spheres

3.2. The Energy of Unit Killing Fields in Dimension 3

3.3. Instability of Hopf Vector Fields

3.4. Existence of Minima in Dimension > 3

3.5. Brito’s Functional

3.6. The Brito Energy of the Reeb Vector

3.7. Vector Fields with Singularities

3.8. Normal Vector Fields on Principal Orbits

3.9. Riemannian Tori

29. Chapter Four. Harmonicity and Contact Metric Structures

4.1. H-Contact Manifolds

4.2. Three-Dimensional H-Contact Manifolds

4.3. Stability of the Reeb Vector Field

4.4. Harmonic Almost Contact Structures

4.5. Reeb Vector Fields on Real Hypersurfaces

4.6. Harmonicity and Stability of the Geodesic Flow

36. Chapter Five. Harmonicity with Respect to g-Natural Metrics

37. Chapter Six. The Energy of Sections

38. Chapter Seven. Harmonic Vector Fields in CR Geometry

39. Chapter Eight. Lorentz Geometry and Harmonic Vector Fields

40. Appendix A. Twisted Cohomologies

41. Appendix B. The Stokes Theorem on Complete Manifolds

42. Appendix C. Complex Monge-Ampère Equations

43. Appendix D. Exceptional Orbits of Highest Dimension

44. Appendix E. Reilly’s Formula

45. References

46. Index