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Inhomogeneous balanced non-Kähler metrics on complex projective spaces
Abstract
We consider the cohomogeneity one action of Gp,q=U(p+1)×U(q+1) on ℂPp+q+1, where p≥ q≥ 1 and p>1. We characterize all Gp,q-invariant Riemannian metrics compatible with the canonical complex structure and obtain parametrizations of the invariant Kähler and balanced metrics. As an application, we use these parametrizations to construct a family of inhomogeneous balanced non-Kähler metrics with positive scalar curvature on complex projective spaces of odd complex dimension.
Related
- New extremal Kähler metrics on projective bundles
- Cohomogeneity one Einstein metrics on complex projective spaces
- Deformations of Kähler and Balanced Hyperbolicity
- Instability of conformally Kähler, Einstein metrics
- Projective embedding of degenerating family of Kähler-Einstein manifolds with normal crossing limit
BibTeX
@misc{grajales2026inhomogeneous,
title = {{Inhomogeneous balanced non-Kähler metrics on complex projective spaces}},
author = {Brian Grajales and Lino Grama},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24116},
eprint = {2610.24116},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24116},
}
RIS
TY - UNPB
TI - Inhomogeneous balanced non-Kähler metrics on complex projective spaces
AU - Brian Grajales
AU - Lino Grama
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24116
UR - https://arxiv.org/abs/2610.24116
AB - We consider the cohomogeneity one action of G_p,q=U(p+1)×U(q+1) on ℂP^p+q+1, where p≥ q≥ 1 and p>1. We characterize all G_p,q-invariant Riemannian metrics compatible with the canonical complex structure and obtain parametrizations of the invariant Kähler and balanced metrics. As an application, we use these parametrizations to construct a family of inhomogeneous balanced non-Kähler metrics with positive scalar curvature on complex projective spaces of odd complex dimension.
ER -