PreprintarXiv licencearXiv
The cross quadratic bisectional curvature of Kähler C-spaces of classical type
Abstract
In this paper, we show that any Kähler C-space of classical type has nonnegative cross quadratic bisectional curvature and positive dual cross quadratic bisectional curvature. As a consequence, such manifolds are Fano. This confirms a substantial part of a conjecture of Ni-Zheng (Conjecture 1.5 in \cite{NZ}).
Related
- Ricci pinching on complete Kähler manifolds with nonnegative bisectional curvature
- Non-strict negativity of holomorphic bisectional curvature for compact relative Kähler fibrations
- Holomorphic Bisectional Curvature on Total Spaces of Holomorphic Vector Bundles
- Holomorphic sectional curvature and the Calabi operator on Kähler C-spaces
- Uniform Quadratic Growth and Second-Order Variational Curvature in Hilbert Spaces
BibTeX
@misc{jian2026cross,
title = {{The cross quadratic bisectional curvature of Kähler $C$-spaces of classical type}},
author = {Run-Qiang Jian and Zhuhong Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39012},
eprint = {2610.39012},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39012},
}
RIS
TY - UNPB
TI - The cross quadratic bisectional curvature of Kähler C-spaces of classical type
AU - Run-Qiang Jian
AU - Zhuhong Zhang
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.39012
UR - https://arxiv.org/abs/2610.39012
AB - In this paper, we show that any Kähler C-space of classical type has nonnegative cross quadratic bisectional curvature and positive dual cross quadratic bisectional curvature. As a consequence, such manifolds are Fano. This confirms a substantial part of a conjecture of Ni-Zheng (Conjecture 1.5 in \cite{NZ}).
ER -