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In this mostly survey paper we will consider Sasaki manifolds M whose regular quotient is of the form \(N={\mathbb P}(E_0 \oplus E_\infty ) \rightarrow S\) , where \(E_0\) and \(E_\infty \) are both projectively flat hermitian holomorphic vector bundles over a compact Kähler manifold S. While N usually does not admit a constant scalar curvature (CSC) Kähler metric, we will see that for an appropriate choice of polarization of N, there always exists a ray of CSC Sasaki metrics somewhere in the Sasaki cone of M. In particular we obtain CSC Sasaki metrics on certain Yamazaki fiber joins over a compact Riemann surface.

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Constant Scalar Curvature Sasaki Metrics

  • 章节

  • 发表日期：

    2025年

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  • Charles P. Boyer,
  • Christina W. Tønnesen-Friedman

摘要

In this mostly survey paper we will consider Sasaki manifolds M whose regular quotient is of the form \(N={\mathbb P}(E_0 \oplus E_\infty ) \rightarrow S\) , where \(E_0\) and \(E_\infty \) are both projectively flat hermitian holomorphic vector bundles over a compact Kähler manifold S. While N usually does not admit a constant scalar curvature (CSC) Kähler metric, we will see that for an appropriate choice of polarization of N, there always exists a ray of CSC Sasaki metrics somewhere in the Sasaki cone of M. In particular we obtain CSC Sasaki metrics on certain Yamazaki fiber joins over a compact Riemann surface.