Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds

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 Kähler-Ricci soliton on ${\mathbb{C}}^n$ which admits no local holomorphic isometry into products of homogeneous bounded domains with flat Kähler manifolds and generalized flag manifolds.

References in corpus (5)

• Kähler immersions of Kähler-Ricci solitons into definite or indefinite complex space forms
• Sasakian immersions of Sasaki-Ricci solitons into Sasakian space forms
• Immersions into Sasakian space forms
• On holomorphic isometries into blow-ups of ${\mathbb{C}}^n$
• Rigidity properties of holomorphic isometries into homogeneous Kähler manifolds