Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds

Author:

Roberto Mossa, Giovanni Placini

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG)

journal:

date:

2023-06-29 16:00:00

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.

PDF: Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds.pdf