Abstract
It is conjectured that the lifted Futaki invariant of an $n$-dimensional compact complex manifold vanishes if it admits an Einstein-Kähler metric. If the conjecture holds for $n = 1$, the lifted Futaki invariants for Riemann surfaces must vanish because Riemann surfaces always admit Einstein-Kähler metrics. In this paper, we prove the vanishing of the lifted Futaki invariants for Riemann surfaces under a certain assumption. Our main result is Theorem 1.3.
Citation
Kenji Tsuboi. "The lifted Futaki invariants for Riemann surfaces." Proc. Japan Acad. Ser. A Math. Sci. 77 (6) 75 - 78, June 2001. https://doi.org/10.3792/pjaa.77.75
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