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.
Publié le : 2001-06-14
Classification:
The lifted Futaki invariant,
complex manifold,
Einstein-Kähler metric,
Riemann surface,
32Q20,
30F99,
58J20
@article{1148479938,
author = {Tsuboi, Kenji},
title = {The lifted Futaki invariants for Riemann surfaces},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {77},
number = {10},
year = {2001},
pages = { 75-78},
language = {en},
url = {http://dml.mathdoc.fr/item/1148479938}
}
Tsuboi, Kenji. The lifted Futaki invariants for Riemann surfaces. Proc. Japan Acad. Ser. A Math. Sci., Tome 77 (2001) no. 10, pp. 75-78. http://gdmltest.u-ga.fr/item/1148479938/