As on arXiv
Abstract
Let be an irreducible non-trivial Kähler gradient Ricci soliton of real dimension . We show that its group of isometries is of dimension at most and the case of equality is characterized. As a consequence, our framework shows the uniqueness of -invariant Kähler gradient Ricci solitons constructed earlier. There are corollaries regarding the groups of automorphisms or affine transformations and a general version for almost Hermitian GRS. The approach is based on a connection to the geometry of an almost contact metric structure.
Comments: accepted for publication in Advances in Mathematics with several small improvements
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The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Kähler-Ricci solitons with almost maximal symmetry
Topics Sasakian & contact geometry, Kähler geometry, Ricci solitons · Same author Hung Tran · Shared terms “isometry”, “gradient Ricci”
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Topics Kähler geometry, Ricci solitons · Same author Hung Tran · Shared terms “Kähler gradient”, “real dimension”, “gradient Ricci”
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Topics Sasakian & contact geometry · Shared terms “metric structure”
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Kählerity of complete almost-Kähler gradient shrinking Ricci solitons
Topics Kähler geometry, Ricci solitons · Shared terms “Kähler gradient”, “real dimension”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.