Twisted and coupled constant scalar curvature K\"{a}hler metrics on minimal ruled surfaces

Ramesh Mete

doi:10.1016/j.bulsci.2025.103748

Twisted and coupled constant scalar curvature K\"{a}hler metrics on minimal ruled surfaces

Differential Geometry 2025-11-04 v3 Complex Variables

Authors: Ramesh Mete

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Abstract

In this paper, we study the existence of twisted constant scalar curvature K\"{a}hler (cscK) metrics and non-existence of coupled cscK metrics on minimal ruled surfaces over a Riemann surface of genus $2$ . Moreover, we give a bound for the Chen-Cheng invariant related to Chen's continuity path for cscK problem on these ruled surfaces.

Keywords

twisted cscK metrics coupled cscK metrics minimal ruled surfaces Chen-Cheng invariant continuity path

Cite

@article{arxiv.2505.23327,
  title  = {Twisted and coupled constant scalar curvature K\"{a}hler metrics on minimal ruled surfaces},
  author = {Ramesh Mete},
  journal= {arXiv preprint arXiv:2505.23327},
  year   = {2025}
}

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