Abstract
In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.
References
[1] M. Abreu, Kähler geometry of toric manifolds in symplectic coordinates, Symplectic and contact topology: interactions and perspectives (Toronto, ON/Montreal, QC, 2001), Fields Inst. Commun., vol. 35, Amer. Math. Soc., Providence, RI, 2003, pp. 1-24.10.1090/fic/035/01Search in Google Scholar
[2] S. Calamai and D. Petrecca, On Calabi extremal Kähler-Ricci solitons, Proc. Amer. Math. Soc. 144 (2016), no. 2, 813-821. MR 3430856Search in Google Scholar
[3] B. Chow et al., The Ricci Flow: Techniques and Applications: Geometric Aspects, Mathematical surveys and monographs, vol. 135, American Mathematical Society, 2007.Search in Google Scholar
[4] S. K. Donaldson, Kähler geometry on toric manifolds, and some other manifolds with large symmetry, Handbook of geometric analysis. No. 1, Adv. Lect. Math. (ALM), vol. 7, Int. Press, Somerville, MA, 2008, pp. 29-75. MR 2483362Search in Google Scholar
[5] F. Podestà and A. Spiro, Kähler-Ricci solitons on homogeneous toric bundles, J. Reine Angew. Math. 642 (2010), 109-127. MR 2658183Search in Google Scholar
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