Ambient constructions for Sasakian $\eta$-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 operators, 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 $\eta$-Einstein manifolds. As an application, we study properties of the first and the second variation of the total $Q$-prime curvature at Sasakian $\eta$-Einstein manifolds.

22 pages, references added, typos corrected

References in corpus (3)

• The Ambient Obstruction Tensor and Q-Curvature
• Variation of total Q-prime curvature on CR manifolds
• Some Remarks on the Total CR $Q$ and $Q^{\prime }$-Curvatures

Cited by in corpus (5)

• Nonnegativity of the CR Paneitz operator for embeddable CR manifolds
• The $P^{\prime }$-operator, the $Q^{\prime }$-curvature, and the CR tractor calculus
• Generalizations of the $Q$-prime curvature via renormalized characteristic forms
• Formulae of some global CR invariants for Sasakian $\eta$-Einstein manifolds
• CR Yamabe constant and inequivalent CR structures