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On strongly convex Kähler--Berwald manifolds
Abstract
For every real Berwald strongly convex complex Finsler manifold (M,F,J,∇̂), if the Cartan nonlinear connection satisfies the parallelism condition ∇̂ J=0, we construct a good complex vertical connection D, prove that D is the complex Rund connection, and F is Kähler-Berwald. The inverse direction also can be seen from the construction and proof. As an application, we prove that on an irreducible Hermitian symmetric space M=G/H, G-invariant complex Finsler metrics are Kähler--Berwald. Besides, we obtain the characterization of strongly pseudoconvex holomorphically invariant complex Finsler metrics on the classical domains of type-IV.
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BibTeX
@misc{ge2026strongly,
title = {{On strongly convex Kähler--Berwald manifolds}},
author = {Xiaoshu Ge},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07752},
eprint = {2611.07752},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07752},
}
RIS
TY - UNPB
TI - On strongly convex Kähler--Berwald manifolds
AU - Xiaoshu Ge
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07752
UR - https://arxiv.org/abs/2611.07752
AB - For every real Berwald strongly convex complex Finsler manifold (M,F,J,∇̂), if the Cartan nonlinear connection satisfies the parallelism condition ∇̂ J=0, we construct a good complex vertical connection D, prove that D is the complex Rund connection, and F is Kähler-Berwald. The inverse direction also can be seen from the construction and proof. As an application, we prove that on an irreducible Hermitian symmetric space M=G/H, G-invariant complex Finsler metrics are Kähler--Berwald. Besides, we obtain the characterization of strongly pseudoconvex holomorphically invariant complex Finsler metrics on the classical domains of type-IV.
ER -