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Properties of biharmonic submanifolds in spheres. (English) Zbl 1195.53080
Summary: We survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature submanifolds in spheres.

MSC:
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C43 Differential geometric aspects of harmonic maps
53C40 Global submanifolds
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