Erratum to: On the spectrum of the Page and the Chen–LeBrun–Weber metrics

1 Erratum to: Ann Glob Anal Geom (2014) 46:87–101 DOI 10.1007/s10455-014-9412-6

Page 94 The linear functions that define the moment polytope associated to the Chen–LeBrun–Weber metric are given by:

$$\begin{aligned} l_{1}(x) = x_{1}, \ l_{2}(x)=x_{2}, \ l_{3}(x)=(a-x_{1}), \ l_{4}(x) = (a-x_{2}), \ l_{5}(x) = (1+a-x_{1}-x_{2}). \end{aligned}$$

Page 94 The constant $c_{1}$ that determines the scalar curvature ${s_{k}(x)=c_{1}(x_{1}+x_{2})+c_{2}}$ is given by:

$$\begin{aligned} c_{1} = \frac{48(1-a^{3})}{a^{6}+6a^{5}+9a^{4}+4a^{3}-3a^{2}-6a+1}. \end{aligned}$$

The constant $c_{2}$ is given correctly. Though the constant $c_{1}$ was stated incorrectly in the paper, all the numerical calculations were made with the correct constants.

Page 95 The integral in the third line of mathematics from the bottom of the page should read

$$\begin{aligned} \frac{1}{18}\int _{M}\left( 4\Lambda s_{k}^{-6}-s^{-3}_{k}\right) \mathrm{d}V_{k}. \end{aligned}$$