Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A SHORT NOTE ON BIHARMONIC SUBMANIFOLDS IN 3-DIMENSIONAL GENERALIZED (𝜅, 𝜇)-MANIFOLDS

  • Sasahara, Toru (Center for Liberal Arts and Sciences Hachinohe Institute of Technology)
  • Received : 2015.04.21
  • Published : 2016.05.31
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Abstract

We characterize proper biharmonic anti-invariant surfaces in 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds with constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of proper biharmonic submanifolds in a certain 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifold. Moreover, we determine 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds which admit a certain kind of proper biharmonic foliation.

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References

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