Sasakian immersions of Sasaki-Ricci solitons into Sasakian space forms

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 $\varphi$-sectional curvature $c$, then $S$ is $\eta$-Einstein and its $\eta$-Einstein constants are rational. Moreover, if $c\le -3$, $S$ 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.

9 pages, comments are welcome

References in corpus (2)

• Existence of Gradient Kahler-Ricci Solitons
• Kähler immersions of Kähler-Ricci solitons into definite or indefinite complex space forms

Cited by in corpus (3)

• Immersions into Sasakian space forms
• Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds
• Any Sasakian structure is approximated by embeddings into spheres