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Pluriclosed deformations of Bismut flat metrics
Abstract
We deform the complex structure of compact simply-connected Bismut flat manifolds, obtaining new complex manifolds that admit pluriclosed metrics but do not admit Bismut flat metrics. This produces genuinely new examples of pluriclosed manifolds while enriching our understanding of the deformation theory of pluriclosed metrics. Moreover, our main result is relevant for the search of pluriclosed solitons and non-trivial Bismut Hermitian Einstein metrics in all dimensions.
Related
- Complete pluriclosed metrics with vanishing Bismut Ricci form on the affine quadric
- Pluriclosed manifolds with parallel Bismut torsion
- Dirichlet deformations, Morse index, and nonlinear symmetry of Ricci-flat Böhm metrics
- A gluing construction of Z-extremal Kähler metrics and new examples of Bismut Hermitian-Einstein $3$-folds
- Deformations of generalized complex structures on 𝒢-flat transitive Courant algebroids
BibTeX
@misc{barbaro2026pluriclosed,
title = {{Pluriclosed deformations of Bismut flat metrics}},
author = {Giuseppe Barbaro},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35313},
eprint = {2609.35313},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35313},
}
RIS
TY - UNPB
TI - Pluriclosed deformations of Bismut flat metrics
AU - Giuseppe Barbaro
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35313
UR - https://arxiv.org/abs/2609.35313
AB - We deform the complex structure of compact simply-connected Bismut flat manifolds, obtaining new complex manifolds that admit pluriclosed metrics but do not admit Bismut flat metrics. This produces genuinely new examples of pluriclosed manifolds while enriching our understanding of the deformation theory of pluriclosed metrics. Moreover, our main result is relevant for the search of pluriclosed solitons and non-trivial Bismut Hermitian Einstein metrics in all dimensions.
ER -