arXiv subjects

Yasuhiro Nakagawa

Publications and source records attributed to Yasuhiro Nakagawa.

3 recordsLinked to original sources

arXiv2025

Modified extremal Kähler metrics and multiplier Hermitian-Einstein metrics

Motivated by the notion of multiplier Hermitian-Einstein metric of type $σ$ introduced by Mabuchi, we introduce the notion of $σ$-extremal Kähler metrics on compact Kähler manifolds, which generalizes Calabi's extremal Kähler metrics. We characterize the existence of this metric in terms of the coercivity of a certain functional on the space of Kähler metrics to show that, on a Fano manifold, the existence of a multiplier Hermitian-Einstein metric of type $σ$ implies the existence of a $σ$-extremal Kähler metric.

math.DG↗

arXiv2022

Multiplier Hermitian-Einstein metrics on Fano manifolds of KSM-type

In this article we focus on multiplier Hermitian-Einstein metrics introduced by Mabuchi which include Kähler-Einstein metrics, Kähler-Ricci solitons and Mabuchi solitons as special cases. We also focus on KSM-manifolds, which are introduced by the first author as toric bundles, to establish a criterion for the existence of multiplier Hermitian-Einstein metrics in terms of KSM-data. An explicit example for a KSM-manifold admitting a family of multiplier Hermitian-Einstein metrics is constructed by using a continuous path connecting a Kähler-Ricci soliton and a Mabuchi soliton.

math.DG↗

arXiv2011

New examples of Sasaki-Einstein manifolds

In this note, stimulated by the existence result of Futaki-Ono-Wang for toric Sasaki-Einstein metrics, we obtain new examples of Sasaki-Einstein metrics on S^1-bundles associated to canonical line bundles of P^1-bundles over Kähler-Einstein Fano manifolds, even though the Futaki's obstruction does not vanish. Here the method of Sakane and Koiso is used, and our examples include non-toric Sasaki-Einstein manifolds.

math.DG↗