## Tohoku Mathematical Journal 2012 June SECOND SERIES VOL. 64, NO. 2

 Tohoku Math. J. 64 (2012), 195-222

Title BIHARMONIC INTEGRAL $\mathcal{C}$-PARALLEL SUBMANIFOLDS IN 7-DIMENSIONAL SASAKIAN SPACE FORMS

Author Dorel Fetcu and Cezar Oniciuc

(Received December 14, 2010, revised June 16, 2011)
Abstract. We find the characterization of maximum dimensional proper-biharmonic integral $\mathcal{C}$-parallel submanifolds of a Sasakian space form and then we classify such submanifolds in a 7-dimensional Sasakian space form. Working in the sphere $\boldsymbol{S}^7$ we explicitly find all 3-dimensional proper-biharmonic integral $\mathcal{C}$-parallel submanifolds. We also determine the proper-biharmonic parallel Lagrangian submanifolds of $\boldsymbol{C}P^3$.

2000 Mathematics Subject Classification. Primary 53C42; Secondary 53B25.

Key words and phrases. Biharmonic submanifolds, Sasakian space forms.