A short note on biharmonic submanifolds in 3-dimensional generalized $(\kappa, \mu)$-manifolds
Bull. Korean Math. Soc. 2016 Vol. 53, No. 3, 723-732
Published online May 31, 2016
Toru Sasahara
Hachinohe Institute of Technology
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
MSC numbers : Primary 53C42; Secondary 53B25
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