Rigidity of Kähler-Finsler Metrics with Constant Radial Curvature

@misc{li2026rigidity,
  title = {{Rigidity of Kähler-Finsler Metrics with Constant Radial Curvature}},
  author = {Jinling Li and Longjie Li and Chunhui Qiu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39989},
  eprint = {2610.39989},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39989},
}

TY  - UNPB
TI  - Rigidity of Kähler-Finsler Metrics with Constant Radial Curvature
AU  - Jinling Li
AU  - Longjie Li
AU  - Chunhui Qiu
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39989
UR  - https://arxiv.org/abs/2610.39989
AB  - In this paper, we prove that a smooth strongly pseudoconvex Kähler--Finsler metric F satisfying the constant radial curvature condition Ω(χ,χ̅)χ=cF^2χ, c∈ℝ∖{0}, is induced by a Hermitian Kähler metric of holomorphic sectional curvature 2c. Under the Abate--Patrizio curvature symmetry ⟨Ω(·,χ̅)χ,χ⟩ =⟨Ω(χ,χ̅)·,χ⟩, this result gives Hermitian rigidity for nonzero constant holomorphic sectional curvature and the classification of complete simply connected metrics of negative curvature. As an application, we show that the Kobayashi metric of a bounded strongly convex domain with smooth boundary is Kähler--Finsler if and only if the domain is biholomorphic to the unit ball. We also prove that the universal cover of a bounded strongly pseudoconvex domain $D $ with smooth boundary is biholomorphic to the unit ball if and only if its Kobayashi metric is a smooth strongly pseudoconvex Kähler--Finsler metric. Furthermore, we give two explicit examples to illustrate the distinction between the weakly Kähler--Finsler and Kähler--Finsler conditions.
ER  -