Distinguished Kähler metrics on Hirzebruch surfaces
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- by Andrew D. Hwang and Santiago R. Simanca PDF
- Trans. Amer. Math. Soc. 347 (1995), 1013-1021 Request permission
Abstract:
Let ${\mathcal {F}_n}$ be a Hirzebruch surface, $n \geqslant 1$. Using the family of extremal metrics on these surfaces constructed by Calabi [1], we study a closely related scale-invariant variational problem, and show that only ${\mathcal {F}_1}$ admits an extremal Kähler metric which is critical for this new functional. Applying a result of Derdzinski [3], we prove that this metric cannot be conformally equivalent to an Einstein metric on ${\mathcal {F}_1}$. When $n = 2$, we show there is a critical orbifold metric on the space obtained from ${\mathcal {F}_2}$ by blowing down the negative section.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 1013-1021
- MSC: Primary 58E11; Secondary 32J27, 53C55
- DOI: https://doi.org/10.1090/S0002-9947-1995-1246528-9
- MathSciNet review: 1246528