CR invariant powers of the sub-Laplacian. (English) Zbl 1076.53048

Gover, A. Rod; Graham, C. Robin

J. Reine Angew. Math. 583, 1-27 (2005).

The CR invariant sub-Laplacian of Jerison-Lee is the subject of interest. The authors construct and study its generalization. Two families of CR invariant differential operators on densities with leading part a power of a sub-Laplacian are derived. The first family is constructed via the Fefferman metric, the second one is derived from the CR tractor calculus. This family includes operators of every positive power, what differs from the conformal case which was investigated in [A. R. Gover, K. Hirachi, J. Am. Math. Soc. 17, No. 2, 389–405 (2004; Zbl 1066.53037)]. The results obtained are applicable in the 3-dimensional case, where the existence theorem is formulated.

Reviewer: Vyacheslav S. Kalnitsky (St. Peterburg)

MSC:

53C21	Methods of global Riemannian geometry, including PDE methods; curvature restrictions
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
32V05	CR structures, CR operators, and generalizations
58J60	Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
53C05	Connections (general theory)

Keywords:

CR manifolds; invariant operators; tractor calculus; sub-Laplacian

Citations:

Zbl 1066.53037