The CR Bochner Identity and Stable Pseudoharmonic Maps on Pseudohermitian Manifolds
Abstract:
In this report, we first derive the CR Bochner identity for energy density of a seudoharmonic map involving an extra third order operator which characterizes CR-pluriharmonic functions. Secondly, we derive the second variational formula for pseudoharmonic maps and the CR Weitzenb\"{o}ck formula for one-forms. Finally, we are able to obtain a vanishing theorem and solve a conjecture that any stable horizontal pseudoharmonic map from the pseudohermitian sphere into any Riemannian manifold must be a constant map. This is served as an CR analogue for stable harmonic maps in an Eulidean sphere.