Tohoku Mathematical Journal
2024
March
SECOND SERIES VOL. 76, NO. 1

Tohoku Math. J.
76 (2024), 127-152

Title MULTIPLIER HERMITIAN-EINSTEIN METRICS ON FANO MANIFOLDS OF KSM-TYPE

Author Yasuhiro Nakagawa and Satoshi Nakamura

(Received April 4, 2022, revised August 4, 2022)
Abstract. 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 with a Mabuchi soliton.

Mathematics Subject Classification. Primary 53C25; Secondary 53C55, 58E11.
Key words and phrases. Multiplier Hermitian-Einstein metrics, KSM-manifolds.

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