PreprintarXiv licencearXiv
An Adjoint Criterion for Left-Invariant m-Modified Conformal Vector Fields on Even-Dimensional Lie Groups
Abstract
For a fixed positive real constant m, a real Lie algebra of even dimension 2k admits a nonzero left-invariant m-modified conformal vector field for some nondegenerate metric if and only if an adjoint operator has a nonzero real eigenvalue. In that case, a solution exists with neutral signature (k,k) and zero conformal factor. As an application, we classify the admissible four-dimensional Lie algebras and metric signatures; the only Lorentzian exceptions among the admissible algebras are aff(ℂ) and the diamond algebra. On a pseudo-Riemannian manifold of arbitrary indefinite signature, a nonzero m-modified conformal vector field forces lightlike geodesic incompleteness, even when its conformal factor is variable.
Related
- Spectral Reconstruction of Hyperbolic Geometry as a Topological Invariant of a Self‑Adjoint Operator
- Scattering of plane waves and a modified Pompeiu criterion
- A bulk--edge correspondence for two-dimensional self-adjoint boundary and interface problems
- Metric Correspondences and Low-Rank Deformations for Conformal and m-Modified Conformal Vector Fields
- On the Dirichlet-to-Neumann conformal invariant of bounded planar domains
BibTeX
@misc{li2026adjoint,
title = {{An Adjoint Criterion for Left-Invariant $m$-Modified Conformal Vector Fields on Even-Dimensional Lie Groups}},
author = {Zhigang Li and Shaoqiang Deng and Hui Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22759},
eprint = {2610.22759},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22759},
}
RIS
TY - UNPB
TI - An Adjoint Criterion for Left-Invariant m-Modified Conformal Vector Fields on Even-Dimensional Lie Groups
AU - Zhigang Li
AU - Shaoqiang Deng
AU - Hui Zhang
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22759
UR - https://arxiv.org/abs/2610.22759
AB - For a fixed positive real constant m, a real Lie algebra of even dimension 2k admits a nonzero left-invariant m-modified conformal vector field for some nondegenerate metric if and only if an adjoint operator has a nonzero real eigenvalue. In that case, a solution exists with neutral signature (k,k) and zero conformal factor. As an application, we classify the admissible four-dimensional Lie algebras and metric signatures; the only Lorentzian exceptions among the admissible algebras are aff(ℂ) and the diamond algebra. On a pseudo-Riemannian manifold of arbitrary indefinite signature, a nonzero m-modified conformal vector field forces lightlike geodesic incompleteness, even when its conformal factor is variable.
ER -