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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
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