Bochner-Kaehler metrics and connections of Ricci type

TL;DR

This paper classifies Bochner-Kaehler metrics using symplectic connection theory, explores their relation to Sasaki metrics, and discusses dualities with Ricci-type metrics, advancing understanding of special geometric structures.

Contribution

It provides a local classification of Bochner-Kaehler metrics via orbit types in $su(n,1)$ and links them to symplectic and Weyl connections, highlighting dualities.

Findings

Classified Bochner-Kaehler metrics based on orbit types in $su(n,1)$

Established relations between Sasaki and Bochner-Kaehler metrics

Outlined connections between symplectic, Weyl, and Ricci-type metrics

Abstract

We apply the results from the article Cahen, Schwachh\"ofer: Special symplectic connections, to the case of Bochner-Kaehler metrics. We obtain a (local) classification of these based on the orbit types of the adjoint action in $su(n,1)$. The relation between Sasaki and Bochner-Kaehler metrics in cone and transveral metrics constructions is discussed. The connection of the special symplectic and Weyl connections is outlined. The duality between the Ricci-type and Bochner-Kaehler metrics is shown.