Harmonic Vector Fields

Chapter Seven. Harmonic Vector Fields in CR Geometry

Contents

7.1 The Canonical Metric 359

7.2 Bundles of Hyperquadrics in ( T( M), J, G_s) 365

7.3 Harmonic Vector Fields from C( M) 377

7.4 Boundary Values of Bergman-Harmonic Maps 387

7.5 Pseudoharmonic Maps 389

7.6 The Pseudohermitian Biegung 394

7.6.1 Total Bending 394

7.6.2 Tangent Bundles over CR Manifolds 395

7.6.3 The First Variation Formula 396

7.6.4 Unboundedness of the Energy Functional 400

7.7 The Second Variation Formula 401

Chapter 7 reports on the development of two analogous theories of pseudoharmonic vector fields (or subelliptic harmonic vector fields) within CR geometry, following the work by D. Perrone et al. (2006) and by Y. Kamishima et al. (2010). In Section 7.1 we describe the canonical ...