Tohoku Mathematical Journal
2001
June
SECOND SERIES VOL. 53, NO. 2

Tohoku Math. J.
53 (2001), 171-182

Title KÄHLER-EINSTEIN METRICS FOR MANIFOLDS WITH NONVANISHING FUTAKI CHARACTER

Author Toshiki Mabuchi

(Received June 16, 1999)
Abstract. In this paper, we generalize the concept of Kähler-Einstein metrics for Fano manifolds with nonvanishing Futaki character. Similar to Kähler-Einstein metrics, these new metrics have various nice properties. In addition, the equations for the metrics are in general neither those of extremal Kähler metrics nor those of Kähler-Ricci solitons.

2000 Mathematics Subject Classification. Primary 53C55; secondary 14J45, 14J50, 32J25.

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