Ambient constructions for Sasakian η-Einstein manifolds
Copyright policy )Ambient constructions for Sasakian η-Einstein manifolds
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 $η$-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.
22 pages, references added, typos corrected
- University of Tokyo Japan
Mathematics - Differential Geometry, CR structures, CR operators, and generalizations, Mathematics - Complex Variables, \(Q\)-prime curvature, Sasakian \(\eta\)-Einstein manifold, \(P\)-prime operator, CR invariant differential operator, Special Riemannian manifolds (Einstein, Sasakian, etc.), Differential Geometry (math.DG), FOS: Mathematics, 32V05, 32V20, Complex Variables (math.CV)
Mathematics - Differential Geometry, CR structures, CR operators, and generalizations, Mathematics - Complex Variables, \(Q\)-prime curvature, Sasakian \(\eta\)-Einstein manifold, \(P\)-prime operator, CR invariant differential operator, Special Riemannian manifolds (Einstein, Sasakian, etc.), Differential Geometry (math.DG), FOS: Mathematics, 32V05, 32V20, Complex Variables (math.CV)
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