PreprintarXiv licencearXiv
Fedosov manifolds with parallel symplectic Weyl curvature
Abstract
A classical 1977 result by Roter states that a Riemannian manifold of dimension at least four with parallel Weyl curvature must be locally symmetric or conformally flat. We establish Roter's theorem in the symplectic category: namely, a Fedosov manifold with parallel symplectic Weyl curvature must be locally symmetric or Weyl-flat.
Related
- Curvature characterization of Hermitian manifolds with Bismut parallel torsion
- Symplectic four-manifolds and hyperbolic π-orbifolds
- The ECH and alternative ECH capacities of closed symplectic 4-manifolds
- Finite Symplectic Automorphisms of Hyperkähler Manifolds of K3[n]-Type Act Trivially on Discriminant Groups
- Mazur manifolds and symplectic structures
BibTeX
@misc{rankin2026fedosov,
title = {{Fedosov manifolds with parallel symplectic Weyl curvature}},
author = {Shane Rankin and Ivo Terek},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.38703},
eprint = {2609.38703},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38703},
}
RIS
TY - UNPB
TI - Fedosov manifolds with parallel symplectic Weyl curvature
AU - Shane Rankin
AU - Ivo Terek
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2609.38703
UR - https://arxiv.org/abs/2609.38703
AB - A classical 1977 result by Roter states that a Riemannian manifold of dimension at least four with parallel Weyl curvature must be locally symmetric or conformally flat. We establish Roter's theorem in the symplectic category: namely, a Fedosov manifold with parallel symplectic Weyl curvature must be locally symmetric or Weyl-flat.
ER -