Proceedings of the Japan Academy, Series A, Mathematical Sciences

The lifted Futaki invariants for Riemann surfaces

Kenji Tsuboi

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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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 77, Number 6 (2001), 75-78.

Dates
First available in Project Euclid: 24 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148479938

Digital Object Identifier
doi:10.3792/pjaa.77.75

Mathematical Reviews number (MathSciNet)
MR1842859

Zentralblatt MATH identifier
0997.32018

Subjects
Primary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx]
Secondary: 30F99: None of the above, but in this section 58J20: Index theory and related fixed point theorems [See also 19K56, 46L80]

Keywords
The lifted Futaki invariant complex manifold Einstein-Kähler metric Riemann surface

Citation

Tsuboi, Kenji. The lifted Futaki invariants for Riemann surfaces. Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 6, 75--78. doi:10.3792/pjaa.77.75. https://projecteuclid.org/euclid.pja/1148479938


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References

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  • Tsuboi, K.: The lifted Futaki invariants and the Spin$^c$-Dirac operators. Osaka J. Math., 32, 207–225 (1995).