English

Mabuchi's soliton metric and relative D-stability

Differential Geometry 2020-01-13 v2 Complex Variables

Abstract

For Fano manifolds T. Mabuchi introduced a generalization of the K\"ahler-Einstein metric, which is characterized as the critical point of the Ricci-Calabi functional. We show that a Fano manifold admits Mabuchi's metric if and only if it is uniformly relatively D-stable.

Keywords

Cite

@article{arxiv.1905.05948,
  title  = {Mabuchi's soliton metric and relative D-stability},
  author = {Tomoyuki Hisamoto},
  journal= {arXiv preprint arXiv:1905.05948},
  year   = {2020}
}

Comments

We fixed the proof of the main theorem in the first version, following the work of Professor C. Li