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A note on biharmonic submanifolds of product spaces

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Abstract

We investigate biharmonic submanifolds of the product of two space forms. We prove a necessary and sufficient 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.

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Correspondence to Julien Roth.

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Roth, J. A note on biharmonic submanifolds of product spaces. J. Geom. 104, 375–381 (2013). https://doi.org/10.1007/s00022-013-0168-0

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Mathematics Subject Classification (2000)

  • 53C42
  • 53C43

Keywords

  • Biharmonic submanifolds
  • product spaces