Harmonic Vector Fields

Chapter Six. The Energy of Sections

Contents

6.1. The Horizontal Bundle 309

6.2. The Sasaki Metric 316

6.3. The Sphere Bundle U( E) 320

6.4. The Energy of Cross Sections 324

6.5. Unit Sections 326

6.6. Harmonic Sections in Normal Bundles 329

6.7. The Energy of Oriented Distributions 332

6.8. Examples of Harmonic Distributions 337

6.9. The Chacon-Naveira Energy 344

6.9.1. Energy of Smooth Distributions 344

6.9.2. The Chacon-Naveira Energy of Distributions on 3-Sasakian Manifolds and Normal Complex Contact Manifolds 346

Chapter 6 is devoted to the study of harmonic sections in vector bundles, in particular in the normal bundle associated to a given isometric immersion. One also computes the energy of oriented distributions (thought of as sections in Grassmann ...