Biharmonic C-parallel Legendrian submanifolds in 7-dimensional Sasakian space forms

TL;DR

This paper completes the classification of biharmonic C-parallel Legendrian submanifolds in 7-dimensional Sasakian space forms by explicitly determining all such submanifolds, extending previous incomplete results.

Contribution

It provides a complete explicit classification of biharmonic C-parallel Legendrian submanifolds in 7-dimensional Sasakian space forms, resolving prior incompleteness.

Findings

Explicit classification of all such submanifolds.

Resolution of previous incomplete classification.

Extension of known results to all cases.

Abstract

In [5], D. Fetcu and C. Oniciuc presented the classification result for biharmonic $\mathcal{C}$-parallel Legendrian submanifolds in $7$-dimensional Sasakian space forms. However, it is incomplete. In this paper, all such submanifolds are explicitly determined.