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arXiv · 2306.17783

Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds

Roberto Mossa·Giovanni Placini
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Abstract

We discuss local Sasakian immersion of Sasaki-Ricci solitons (SRS) into fiber products of homogeneous Sasakian manifolds. In particular, we prove that SRS locally induced by a large class of fiber products of homogeneous Sasakian manifolds are, in fact, $\eta$-Einstein. The results are stronger for immersions into Sasakian space forms. Moreover, we show an example of a K\"ahler-Ricci soliton on $\mathbb C^n$ which admits no local holomorphic isometry into products of homogeneous bounded domains with flat K\"ahler manifolds and generalized flag manifolds.

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Roberto Mossa, Giovanni Placini. 2023-06-30. Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds. https://doi.org/10.1007/s10455-023-09939-4

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