## Biharmonic integral $$\mathcal{C}$$-parallel submanifolds in 7-dimensional Sasakian space forms.(English)Zbl 1258.53059

Summary: 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 $${S}^7$$ we explicitly find all 3-dimensional proper-biharmonic integral $$\mathcal{C}$$-parallel submanifolds. We also determine the proper-biharmonic parallel Lagrangian submanifolds of $$\mathbb{C}P^3$$.

### MSC:

 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53B25 Local submanifolds 53C30 Differential geometry of homogeneous manifolds

### Keywords:

biharmonic submanifolds; Sasakian space forms
Full Text:

### References:

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