PreprintarXiv licencearXiv
On the Definition and Smooth Examples of Weakly Kähler--Finsler Metrics
Abstract
The generalization of the Kähler metric in the complex Finsler setting admits four natural versions. Among these, the strongly Kähler--Finsler condition is known to coincide with one of the intermediate conditions. In this paper, we establish the equivalence between the weakly Kähler--Finsler condition and the remaining intermediate condition. Moreover, we obtain new necessary and sufficient conditions for a weakly Kähler--Finsler metric to be strongly Kähler--Finsler. Using these criteria, we construct, for the first time, smooth examples of weakly Kähler--Finsler metrics which are not Kähler--Finsler, via the Kobayashi metrics on smooth bounded strongly convex domains.
Related
- Kähler-Finsler rigidity of the Kobayashi metric and the Kähler base of weakly Kähler-Finsler metrics
- A Demailly-type approximation of singular Finsler metrics
- Spherically symmetric Finsler metrics satisfying the σT-condition
- Conformal boundary rigidity for simple Finsler metrics
- Isoperimetric problem for quasi-Finsler metrics and shapes of least aerodynamic resistance
BibTeX
@misc{ge2026definition,
title = {{On the Definition and Smooth Examples of Weakly Kähler--Finsler Metrics}},
author = {Xiaoshu Ge},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03535},
eprint = {2610.03535},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03535},
}
RIS
TY - UNPB
TI - On the Definition and Smooth Examples of Weakly Kähler--Finsler Metrics
AU - Xiaoshu Ge
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03535
UR - https://arxiv.org/abs/2610.03535
AB - The generalization of the Kähler metric in the complex Finsler setting admits four natural versions. Among these, the strongly Kähler--Finsler condition is known to coincide with one of the intermediate conditions. In this paper, we establish the equivalence between the weakly Kähler--Finsler condition and the remaining intermediate condition. Moreover, we obtain new necessary and sufficient conditions for a weakly Kähler--Finsler metric to be strongly Kähler--Finsler. Using these criteria, we construct, for the first time, smooth examples of weakly Kähler--Finsler metrics which are not Kähler--Finsler, via the Kobayashi metrics on smooth bounded strongly convex domains.
ER -