Generalized scalar curvature and Ricci flow on compact Lie groups
Abstract
Let G be a compact connected semisimple Lie group, let Q be a bi-invariant metric and let ρ be its Cartan three-form. We prove that every left-invariant generalized Ricci flow with [H0]=[ρ] exists for all positive time and converges smoothly to a Bismut-Ricci-flat pair without rescaling or pullback. The standard pair uniquely maximizes generalized scalar curvature in its torsion class, and every left-invariant Bismut-Ricci-flat pair on a compact simple group is standard, answering questions of Fusi, Lafuente and Stanfield and of Lauret and Will. On the product of two copies of a compact simple group, nonstandard stationary pairs in the Cartan class are known; we construct nonstationary flows with the exact initial form [H0]=[ρ] and nonstandard limits, disproving the general semisimple case of the convergence conjecture of Garcia-Fernandez and Streets. The proofs use a proper nonincreasing energy and a decomposition of Killing fields that parametrizes the stationary pairs by nilpotent Lie algebra endomorphisms.
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BibTeX
@misc{chen2026generalized,
title = {{Generalized scalar curvature and Ricci flow on compact Lie groups}},
author = {Zhiqi Chen and Jianhua Yu and Huibin Chen and Junna Ni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03795},
eprint = {2610.03795},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03795},
}
RIS
TY - UNPB
TI - Generalized scalar curvature and Ricci flow on compact Lie groups
AU - Zhiqi Chen
AU - Jianhua Yu
AU - Huibin Chen
AU - Junna Ni
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03795
UR - https://arxiv.org/abs/2610.03795
AB - Let G be a compact connected semisimple Lie group, let Q be a bi-invariant metric and let ρ be its Cartan three-form. We prove that every left-invariant generalized Ricci flow with [H_0]=[ρ] exists for all positive time and converges smoothly to a Bismut-Ricci-flat pair without rescaling or pullback. The standard pair uniquely maximizes generalized scalar curvature in its torsion class, and every left-invariant Bismut-Ricci-flat pair on a compact simple group is standard, answering questions of Fusi, Lafuente and Stanfield and of Lauret and Will. On the product of two copies of a compact simple group, nonstandard stationary pairs in the Cartan class are known; we construct nonstationary flows with the exact initial form [H_0]=[ρ] and nonstandard limits, disproving the general semisimple case of the convergence conjecture of Garcia-Fernandez and Streets. The proofs use a proper nonincreasing energy and a decomposition of Killing fields that parametrizes the stationary pairs by nilpotent Lie algebra endomorphisms.
ER -