On the variation of the Einstein-Hilbert action in pseudohermitian geometry

2023/06/13 by Afeltra, Claudio, Cheng, Jih-Hsin, Malchiodi, Andrea +1 · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.07523

Abstract

In this paper we compute the first and second variation of the normalized Einstein-Hilbert functional on CR manifolds. We characterize critical points as pseudo-Einstein structures. We then turn to the second variation on standard spheres. While the situation is quite similar to the Riemannian case in dimension greater or equal to five, in three dimension we observe a crucial difference, which mainly depends on the embeddable character of the perturbed CR structure.

Cited by

• The toric CR Yamabe problem

Related

• A characterization of homogeneous three-dimensional CR manifolds
• On a remarkable formula of Jerison and Lee in CR geometry
• Pseudo-Einstein structure, eigenvalue estimate for the CR Paneitz operator and its applications to uniformization theorem
• Second Variation of F-Einstein-Hilbert Functional
• On the pseudohermitian sectional curvature of a strictly pseudoconvex CR manifold