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Canonical Bochner-Kähler potentials via the Sasaki-Kähler correspondence

  • Martin Kolář
  • Gerd Schmalz
  • David Sykes
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Abstract

We introduce a new approach to the study of Bochner-Kähler manifolds, based on normal form techniques in CR geometry. As observed by Webster, Bochner-Kähler manifolds are intimately related to spherical Sasakian manifolds. Our approach utilises this relationship as well as normal forms for spherical Sasakian manifolds (known as rigid spheres). In this setting potentials of Bochner-Kähler manifolds are nothing but the defining equations of rigid spheres in rigid normal form. This leads to a canonical formula for Bochner-Kähler potentials, as well as streamlined proofs of known results on the structure and the symmetries of Bochner-Kähler manifolds. Our approach also provides a host of examples in terms of an implicit formula of the corresponding Kähler potentials.

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Cite

BibTeXRIS
BibTeX
@misc{kolar2026canonical,
  title = {{Canonical Bochner-Kähler potentials via the Sasaki-Kähler correspondence}},
  author = {Martin Kolář and Gerd Schmalz and David Sykes},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03791},
  eprint = {2609.03791},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03791},
}
RIS
TY  - UNPB
TI  - Canonical Bochner-Kähler potentials via the Sasaki-Kähler correspondence
AU  - Martin Kolář
AU  - Gerd Schmalz
AU  - David Sykes
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03791
UR  - https://arxiv.org/abs/2609.03791
AB  - We introduce a new approach to the study of Bochner-Kähler manifolds, based on normal form techniques in CR geometry. As observed by Webster, Bochner-Kähler manifolds are intimately related to spherical Sasakian manifolds. Our approach utilises this relationship as well as normal forms for spherical Sasakian manifolds (known as rigid spheres). In this setting potentials of Bochner-Kähler manifolds are nothing but the defining equations of rigid spheres in rigid normal form. This leads to a canonical formula for Bochner-Kähler potentials, as well as streamlined proofs of known results on the structure and the symmetries of Bochner-Kähler manifolds. Our approach also provides a host of examples in terms of an implicit formula of the corresponding Kähler potentials.
ER  -