Subelliptic biharmonic maps

TL;DR

This paper investigates subelliptic biharmonic maps from CR manifolds into Riemannian manifolds, establishing a characterization via lifts to the Fefferman metric, thus linking subelliptic and biharmonic map theories.

Contribution

It provides a new characterization of subelliptic biharmonic maps through their lifts to the Fefferman metric, connecting CR geometry with biharmonic map theory.

Findings

A map is subelliptic biharmonic iff its lift is biharmonic with respect to the Fefferman metric.

Establishes a correspondence between subelliptic biharmonic maps and biharmonic maps on the circle bundle.

Bridges the gap between subelliptic analysis and biharmonic map theory.

Abstract

We study subelliptic biharmonic maps, i.e. smooth maps from a compact strictly pseudoconvex CR manifold M into a Riemannian manifold N which are critical points of a certain bienergy functional. We show that a map is subelliptic biharmonic if and only if its vertical lift to the (total space of the) canonical circle bundle is a biharmonic map with respect to the Fefferman metric.