Integrable sigma model with generalized F structure, Yang-Baxter sigma model with generalized complex structure and multi-Yang-Baxter sigma model

We construct an integrable sigma model with a generalized $F$ structure, which involves a generalized Nijenhuis structure $J$ satisfying $J^3=-J$. Utilizing the expression of the generalized complex structure on the metric Lie group manifold G in terms of operator relations on its Lie algebra $g$, we formulate a Yang-Baxter sigma model with a generalized complex structure. Additionally, we present multi-Yang-Baxter sigma models featuring two and three compatible Nijenhuis structures. Examples for each of these models are provided.