Ambient constructions for Sasakian η-Einstein manifolds

Abstract

The theory of ambient spaces is useful to define CR invariant objects, such as CR invariant powers of the sub-Laplacian, the P-prime operator, and Q-prime curvature. However in general, it is difficult to write down these objects in terms of the Tanaka–Webster connection. In this paper, we give those explicit formulas for CR manifolds satisfying an Einstein condition, called Sasakian η-Einstein manifolds. As an application, we study properties of the first and the second variation of the total Q-prime curvature at Sasakian η-Einstein manifolds.