The rigidity of conformal circle-preserving transformations on Berwaldian manifolds

Zohreh Fathi; Sajjad Lakzian

The rigidity of conformal circle-preserving transformations on Berwaldian manifolds

Differential Geometry 2026-07-01 v1 Analysis of PDEs Metric Geometry

Authors: Zohreh Fathi , Sajjad Lakzian

Abstract

We prove that a complete Berwaldian manifold $\left(M,F\right)$ admitting a nontrivial conformal circle preserving transformation (\cpt for short) must be Riemannian, provided that it has a dense subset on which no flag curvature vanishes (in particular, if $(M,F)$ has positive or negative flag curvature).

Keywords

Berwald manifolds conformal transformations circle-preserving rigidity flag curvature

Cite

@article{arxiv.2607.01350,
  title  = {The rigidity of conformal circle-preserving transformations on Berwaldian manifolds},
  author = {Zohreh Fathi and Sajjad Lakzian},
  journal= {arXiv preprint arXiv:2607.01350},
  year   = {2026}
}

Comments

15 pages