On classification of Finslerian spaces with nontrivial concircular transformations

Zohreh Fathi; Sajjad Lakzian

On classification of Finslerian spaces with nontrivial concircular transformations

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

Authors: Zohreh Fathi , Sajjad Lakzian

Abstract

We prove that in a non-trivial conformal circle-preserving transformation (CPT for short), $e^{\sigma}F$ on a (forward or backward) complete Finslerian manifold $(M,F)$ , the conformal factor has at most two critical points. Then a diffeomorphism classification based on the number of critical points as well as some curvature rigidity properties - of Finslerian manifolds that admit nontrivial conformal CPTs - is presented.

Keywords

Finslerian spaces conformal circle-preserving transformations critical points classification curvature rigidity

Cite

@article{arxiv.2607.05821,
  title  = {On classification of Finslerian spaces with nontrivial concircular transformations},
  author = {Zohreh Fathi and Sajjad Lakzian},
  journal= {arXiv preprint arXiv:2607.05821},
  year   = {2026}
}

Comments

18 pages