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arXiv · 2311.18754

Projectively induced K\"ahler cones over regular Sasakian manifolds

Stefano Marini·Nicoletta Tardini·Michela Zedda
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Abstract

Motivated by a conjecture in [9] we prove that the K\"ahler cone over a regular complete Sasakian manifold is Ricci-flat and projectively induced if and only if it is flat. We also obtain that, up to $\mathcal D_a$-homothetic transformations, K\"ahler cones over homogeneous compact Sasakian manifolds are projectively induced. As main tool we provide a relation between the K\"ahler potentials of the transverse K\"ahler metric and of the cone metric.

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Stefano Marini, Nicoletta Tardini, Michela Zedda. 2023-11-30. Projectively induced K\"ahler cones over regular Sasakian manifolds. https://arxiv.org/abs/2311.18754

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