On the variation of the Einstein–Hilbert action in pseudohermitian geometry-Reference-Cited by-同舟云学术

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

Published:2024-06-04 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Afeltra Claudio¹,Cheng Jih-Hsin²,Malchiodi Andrea³,Yang Paul⁴,Wang Xiaodong⁵

Affiliation:

1. Dipartimento di Matematica , 19034 Università di Trento , Via Sommarive, 14 – 38123 Povo , Italy

2. Institute of Mathematics , Academia Sinica and NCTS 6F, Astronomy-Mathematics Building No. 1, Sec. 4 Roosevelt Road , Taipei 10617 , Taiwan

3. Classe di Scienze , 226478 Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa , Italy

4. Department of Mathematics , Princeton University , Fine Hall, Washington Road , Princeton , NJ 08544-1000 , USA

5. Department of Mathematics , Michigan State University , 619 Red Cedar Road , East Lansing , MI 48824 , USA

Abstract

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.

Funder

Ministry of Science and Technology, Taiwan

National Science Foundation

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2024-0031/pdf

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