Tohoku Mathematical Journal

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

Dorel Fetcu and Cezar Oniciuc

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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 $\boldsymbol{C}P^3$.

Article information

Source
Tohoku Math. J. (2), Volume 64, Number 2 (2012), 195-222.

Dates
First available in Project Euclid: 2 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1341249371

Digital Object Identifier
doi:10.2748/tmj/1341249371

Mathematical Reviews number (MathSciNet)
MR2948819

Zentralblatt MATH identifier
1258.53059

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53B25: Local submanifolds [See also 53C40]

Keywords
Biharmonic submanifolds Sasakian space forms

Citation

Fetcu, Dorel; Oniciuc, Cezar. Biharmonic integral $\mathcal{C}$-parallel submanifolds in 7-dimensional Sasakian space forms. Tohoku Math. J. (2) 64 (2012), no. 2, 195--222. doi:10.2748/tmj/1341249371. https://projecteuclid.org/euclid.tmj/1341249371


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