Constant Scalar Curvature Sasaki Metrics

Charles P. Boyer () and Christina W. Tønnesen-Friedman ()
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Charles P. Boyer: University of New Mexico, Department of Mathematics and Statistics
Christina W. Tønnesen-Friedman: Union College, Department of Mathematics

A chapter in Real and Complex Geometry, 2025, pp 75-92 from Springer

Abstract: Abstract In this mostly survey paper we will consider Sasaki manifolds M whose regular quotient is of the form N = ℙ ( E 0 ⊕ E ∞ ) → S $$N={\mathbb P}(E_0 \oplus E_\infty ) \rightarrow S$$ , where E 0 $$E_0$$ and E ∞ $$E_\infty $$ 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.

Keywords: Constant scalar curvature Sasaki metrics; Yamazaki fiber joins (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-92297-8_3

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DOI: 10.1007/978-3-031-92297-8_3

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