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arXiv · 2102.02523

Sasakian immersions of Sasaki-Ricci solitons into Sasakian space forms

Giovanni Placini
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Abstract

Let $(g,X)$ be a Sasaki-Ricci soliton on a Sasakian manifold $S$. We prove that if $(S,g)$ admits a local Sasakian immersion in a Sasakian space form $S(N,c)$ of constant $\phi$-sectional curvature $c$, then $S$ is $\eta$-Einstein and its $\eta$-Einstein constants are rational. Moreover, if $c\leq -3$, $S$ is locally equivalent to the Sasakian space form $S(n,c)$ and its $\eta$-Einstein constants are determined by $c$. Further results are obtained in the compact setting, i.e. when $c>-3$, under additional hypotheses.

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Giovanni Placini. 2021-02-04. Sasakian immersions of Sasaki-Ricci solitons into Sasakian space forms. https://doi.org/10.1016/j.geomphys.2021.104265

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