New results toward the classification of biharmonic submanifolds in \(\mathbb S^n\) (Q2859478)

The authors prove several rigidity results for biharmonic submanifolds in spheres. They distinguish four specific classes of biharmonic immersions: B1 -- inclusion of a small sphere of radius \(1/\sqrt{2}\) into a unit sphere; B2 -- canonical inclusion of the product of small spheres into a unit sphere; B3 -- a minimal immersion into a small sphere followed by inclusion into a unit sphere; B4 -- the product of minimal immersions into a product of small spheres followed by an inclusion into the unit sphere. The rigidity results assert that different types of biharmonic immersions belong to one of the classes B1--B4.