A note on biharmonic submanifolds of product spaces

Julien Roth (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We investigate biharmonic submanifolds of the product of two space forms. We prove a necessary and suifficent condition for biharmonic submanifolds in these product spaces. Then, we obtain mean curvature estimates for proper-biharmonic submanifold of a product of two unit spheres. We also prove a non-existence result in the case of the product of a sphere and a hyperbolic space.

Mots clés: biharmonic submanifolds; product spaces

Domaines: Géométrie différentielle [math.DG]

Julien Roth. A note on biharmonic submanifolds of product spaces. Journal of Geometry, 2013, 104 (2), pp.375-381. ⟨hal-00827336v2⟩