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 ϕ-sectional curvature c, then S is η-Einstein and its η-Einstein constants are a linear function of c with rational coefficients. Moreover, if c≤−3, S is locally equivalent to the Sasakian space form S(n,c). Further results are obtained in the compact setting, i.e. when c>−3, under additional hypotheses.