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arXiv · 2609.03791

Canonical Bochner-K\"ahler potentials via the Sasaki-K\"ahler correspondence

Martin Kolář·Gerd Schmalz·David Sykes
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Abstract

We introduce a new approach to the study of Bochner-K\"ahler manifolds, based on normal form techniques in CR geometry. As observed by Webster, Bochner-K\"ahler 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-K\"ahler manifolds are nothing but the defining equations of rigid spheres in rigid normal form. This leads to a canonical formula for Bochner-K\"ahler potentials, as well as streamlined proofs of known results on the structure and the symmetries of Bochner-K\"ahler manifolds. Our approach also provides a host of examples in terms of an implicit formula of the corresponding K\"ahler potentials.

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Martin Kolář, Gerd Schmalz, David Sykes. 2026-09-03. Canonical Bochner-K\"ahler potentials via the Sasaki-K\"ahler correspondence. https://arxiv.org/abs/2609.03791

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