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

Claudio Afeltra; Jih Hsin Cheng; Andrea Malchiodi; Paul Yang; Xiaodong Wang

doi:10.1515/crelle-2024-0031

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

Claudio Afeltra, Jih Hsin Cheng, Andrea Malchiodi, Paul Yang, Xiaodong Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 than or equal to five, in three dimensions, we observe a crucial difference, which mainly depends on the embeddable character of the perturbed CR structure.

Original language	English (US)
Pages (from-to)	81-102
Number of pages	22
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2024
Issue number	813
DOIs	https://doi.org/10.1515/crelle-2024-0031
State	Published - Aug 1 2024

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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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 than or equal to five, in three dimensions, we observe a crucial difference, which mainly depends on the embeddable character of the perturbed CR structure.",

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AU - Malchiodi, Andrea

AU - Yang, Paul

AU - Wang, Xiaodong

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AB - 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 than or equal to five, in three dimensions, we observe a crucial difference, which mainly depends on the embeddable character of the perturbed CR structure.

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

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