K\"{a}hler Gradient Ricci Solitons with Large Symmetry

Hung Tran

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arXiv · 2306.05787

K\"{a}hler Gradient Ricci Solitons with Large Symmetry

Hung Tran

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Abstract

Let $(M, g, J, f)$ be an irreducible non-trivial K\"{a}hler gradient Ricci soliton of real dimension $2n$. We show that its group of isometries is of dimension at most $n^2$ and the case of equality is characterized. As a consequence, our framework shows the uniqueness of $U(n)$-invariant K\"{a}hler 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.

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Hung Tran. 2023-06-09. K\"{a}hler Gradient Ricci Solitons with Large Symmetry. https://arxiv.org/abs/2306.05787

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