Chapter Seven - Harmonic Vector Fields in CR Geometry

Abstract

Listen

Translate article

This monograph of tangent sphere bundle carries a natural Riemannian metric naturally associated to the Riemannian metric of a compact orientable n-dimensional Riemannian manifold. The stability problem has not been studied in full generality yet in light of a classical result and taking into account the formal similarity between the shape operator of a sphere and that of tangent sphere bundle, one may expect instability. This chapter reports the development of two analogous theories of pseudoharmonic vector fields (or subelliptic harmonic vector fields) within CR geometry. Subelliptic harmonic vector fields generalize pseudoharmonic maps very much the way harmonic vector fields generalize harmonic maps (within Riemannian or Lorentzian geometry).