A short survey on $\delta$-ideal CR submanifolds

TL;DR

This survey reviews known results on $\delta$-ideal CR submanifolds across various complex space forms and spheres, highlighting their geometric properties and connections to variational problems like the $\lambda$-bienergy.

Contribution

It compiles and discusses existing research on $\delta$-ideal CR submanifolds and explores their relation to critical points of the $\lambda$-bienergy functional.

Findings

Summarizes key properties of $\delta$-ideal CR submanifolds.

Explores the link between $\delta$-ideal CR submanifolds and $\lambda$-bienergy critical points.

Provides insights into variational problems related to these submanifolds.

Abstract

This paper surveys some of the known results on $\delta$-ideal CR submanifolds in complex space forms, the nearly K\"{a}hler $6$-sphere and odd dimensional unit spheres. In addition, the relationship between $\delta$-ideal CR submanifolds and critical points of the $\lambda$-bienergy is mentioned. Some topics on variational problem for the $\lambda$-bienergy are also presented.