PreprintCC0arXiv
Smooth Quasi--Einstein Lifts of Locally Embeddable Three-Dimensional CR Manifolds
Abstract
We prove a C∞ analogue of the real-analytic quasi--Einstein lifting theorem of Hill, Lewandowski and Nurowski \cite[Theorem~2.5]{HLN2008}. Every smooth, locally CR-embeddable, strictly pseudoconvex three-dimensional CR manifold admits, for each real cosmological constant, a local smooth Lorentzian quasi--Einstein lift whose null congruence is geodesic, shearfree and twisting and whose Weyl tensor has Petrov type~II or D. The result extends local lifting beyond the Sasakian setting of the global constructions in \cite{GSS2020} and the local results in \cite{GGS2026}. The proof establishes smooth local solvability of the reduced semilinear contact equation by combining an L∞ contraction with subelliptic regularity.
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BibTeX
@misc{ganji2026smooth,
title = {{Smooth Quasi--Einstein Lifts of Locally Embeddable Three-Dimensional CR Manifolds}},
author = {Masoud Ganji},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24455},
eprint = {2610.24455},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24455},
note = {CC0},
}
RIS
TY - UNPB
TI - Smooth Quasi--Einstein Lifts of Locally Embeddable Three-Dimensional CR Manifolds
AU - Masoud Ganji
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24455
UR - https://arxiv.org/abs/2610.24455
AB - We prove a C^∞ analogue of the real-analytic quasi--Einstein lifting theorem of Hill, Lewandowski and Nurowski \cite[Theorem~2.5]{HLN2008}. Every smooth, locally CR-embeddable, strictly pseudoconvex three-dimensional CR manifold admits, for each real cosmological constant, a local smooth Lorentzian quasi--Einstein lift whose null congruence is geodesic, shearfree and twisting and whose Weyl tensor has Petrov type~II or D. The result extends local lifting beyond the Sasakian setting of the global constructions in \cite{GSS2020} and the local results in \cite{GGS2026}. The proof establishes smooth local solvability of the reduced semilinear contact equation by combining an L^∞ contraction with subelliptic regularity.
ER -