Deformed Gauduchon-Yamabe problems on compact Hermitian manifolds
Abstract
We study a two-parameter deformation of scalar curvature associated with the Gauduchon connections on compact Hermitian manifolds. A central identity expresses its dependence on the connection parameter through the squared norm of the trace-free part of the torsion of the Chern connection. We establish existence criteria for metrics of constant deformed scalar curvature and analyze the global dependence of the deformed Yamabe invariant on the connection parameter, including when the critical threshold is reached. We also study a prescribed-curvature problem in positive conformal classes. Applications include attainment of the critical threshold for an explicit Hopf example in every complex dimension at least two and on non-locally conformally Kähler Iwasawa products.
Related
- A note on the Chern-Yamabe flow on compact Hermitian manifolds with negative Gauduchon degree
- Yamabe-type problems on compact Hermitian manifolds
- Compact lcK manifolds with Gauduchon parallel vector fields
- Smoothness of bounded solutions to complex Hessian equations on compact Hermitian manifolds
- Generalized Gauduchon metrics on compact complex spaces
BibTeX
@misc{windare2026deformed,
title = {{Deformed Gauduchon-Yamabe problems on compact Hermitian manifolds}},
author = {Oluwagbenga Joshua Windare},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38551},
eprint = {2609.38551},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38551},
}
RIS
TY - UNPB
TI - Deformed Gauduchon-Yamabe problems on compact Hermitian manifolds
AU - Oluwagbenga Joshua Windare
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38551
UR - https://arxiv.org/abs/2609.38551
AB - We study a two-parameter deformation of scalar curvature associated with the Gauduchon connections on compact Hermitian manifolds. A central identity expresses its dependence on the connection parameter through the squared norm of the trace-free part of the torsion of the Chern connection. We establish existence criteria for metrics of constant deformed scalar curvature and analyze the global dependence of the deformed Yamabe invariant on the connection parameter, including when the critical threshold is reached. We also study a prescribed-curvature problem in positive conformal classes. Applications include attainment of the critical threshold for an explicit Hopf example in every complex dimension at least two and on non-locally conformally Kähler Iwasawa products.
ER -