On classification of Finslerian spaces with nontrivial concircular transformations

Zohreh Fathi; Sajjad Lakzian

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arXiv · 2607.05821

On classification of Finslerian spaces with nontrivial concircular transformations

Zohreh Fathi·Sajjad Lakzian

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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.

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Zohreh Fathi, Sajjad Lakzian. 2026-07-07. On classification of Finslerian spaces with nontrivial concircular transformations. https://arxiv.org/abs/2607.05821

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