PreprintCC BY 4.0arXiv
Pinching and Tensorial Rigidity for Ergodicity of Frame Flows
Abstract
Let (Mn,g) be a closed, connected, oriented Riemannian manifold with negative sectional curvature and n≥ 2. It is known, due to Brin and Gromov, that the oriented frame flow is ergodic in every odd dimension n≥ 3, n≠ 7. We prove that if a closed, connected, oriented negatively curved Riemannian manifold is strictly quarter-pinched, then its oriented frame flow is ergodic.
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BibTeX
@misc{zhang2026pinching,
title = {{Pinching and Tensorial Rigidity for Ergodicity of Frame Flows}},
author = {Heng Zhang and Shuhao Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.09600},
eprint = {2608.09600},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.09600},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pinching and Tensorial Rigidity for Ergodicity of Frame Flows
AU - Heng Zhang
AU - Shuhao Zhang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2608.09600
UR - https://arxiv.org/abs/2608.09600
AB - Let (M^n,g) be a closed, connected, oriented Riemannian manifold with negative sectional curvature and n≥ 2. It is known, due to Brin and Gromov, that the oriented frame flow is ergodic in every odd dimension n≥ 3, n≠ 7. We prove that if a closed, connected, oriented negatively curved Riemannian manifold is strictly quarter-pinched, then its oriented frame flow is ergodic.
ER -