Biharmonic integral $\mathcal{C}$-parallel submanifolds in 7-dimensional Sasakian space forms

TL;DR

This paper characterizes and classifies proper-biharmonic integral -parallel submanifolds in 7-dimensional Sasakian space forms, explicitly identifying all such submanifolds in  and .

Contribution

It provides a complete classification of proper-biharmonic integral -parallel submanifolds in 7-dimensional Sasakian space forms, including explicit examples in  and .

Findings

Characterization of maximum dimensional proper-biharmonic integral -parallel submanifolds.

Explicit identification of all 3-dimensional proper-biharmonic integral -parallel submanifolds in .

Determination of proper-biharmonic parallel Lagrangian submanifolds in .

Abstract

We find the characterization of maximum dimensional proper-biharmonic integral $\mathcal{C}$-parallel submanifolds of a Sasakian space form and then classify such submanifolds in a 7-dimensional Sasakian space form. Working in the sphere $\mathbb{S}^7$ we explicitly find all 3-dimensional proper-biharmonic integral $C$-parallel submanifolds. We also determine the proper-biharmonic parallel Lagrangian submanifolds of $\mathbb{C}P^3$.