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http://dx.doi.org/10.4134/BKMS.b150275

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)

Publication Information

Bulletin of the Korean Mathematical Society / v.53, no.3, 2016 , pp. 723-732 More about this Journal

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.

Keywords

biharmonic submanifolds; Legendre curves; anti-invariant surfaces; generalized ( ${\kappa}$ , ${\mu}$ )-manifolds;

Citations & Related Records

Reference

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